It is an oft-heard belief that immigrants who come to 'our' country don't "don't make the effort to 'learn' our language'.
As someone who's been an immigrant now for over six years (excluding the fact that I was living in England for many years, which for me is a foreign country) I can offer some suggestions; some of which may apply to the issue of 'not learning the language':
1. They lack confidence with the language
It requires confidence to speak a foreign language. One will have to be prepared to make mistakes that other people will notice. One will not look as intelligent as one does when one speaks ones first language. It requires the taking of a risk to speak with people in 'their' language. Not everyone can take this risk, or take it on a regular basis.
2. They get frustrated with being unable to articulate themselves as they would like to
In a party I held when being relatively new in Poland I was required to speak English as there were people there who spoke no Polish. A friend said, 'You're a lot funnier when you speak English'. The whole business of articulating humour, complex opinions and dealing with a more varied vocabulary than 'I would like some rye bread, please' requires one to have a very good understanding of the language. In the foreign language one tends to appear less intelligent than one would in ones first language. One cannot say things that one wants to say, and this leads to either (a) not saying owt, or (b) reverting to ones first language.
3. Because indigenous dwellers make the whole thing harder
a. They have power
People who are living in the country they were born and bred in have a clear advantage over immigrants. They are 'home'. They hold the power with the language. They are used to using any words they like, as fast as they wish; as unclear as they wish. People who share such a power are likely to understand them. Talking with people who do not speak the language as well as them requires of them the ability to:
Speak slower than normal
Simplify the language
Listen with patience
Ask questions when one is not sure what the other person meant
Try to understand what the other person is saying
In a normal everyday life the indigenous person does not need to use these abilities; they are accustomed to speaking 'normally' and expecting the other person to have the same level of language they have.
I have had people downright refusing to speak slower to me after I had asked them to do so, as they 'cannot speak slower'. I have also had people starting to speak slower, but soon breaking into a more usual tempo after some time. Polish people have done this with me. I do this as well. It is normal.
b. Indigenous dwellers want to speak the foreign language
As an English speaker I often have the experience where, even if I speak Polish or German to them, they answer back in English. Recently someone rung up, and I answered 'Sucham'. The other person said 'Shall I speak English or Polish?'. I said 'Własnie mowiłem po polsku'. She replied 'Shall I speak English?' and so on. Despite being fluent in German I occasionally have Germans speaking English to me. In both cases, the reasons for people doing this are:
They are trying to be friendly
They thought you were speaking your first language (when one has a strong accent this can be the case)
They assume that your ability to speak 'their' language is poor
They want to practice their foreign languages ability
It's mad, sometimes. I have had German and Polish people insisting on speaking English to me, even though it is very clear that my German or Polish is better than their English. Once at a kiosk in Germany a man insisted in replying in English to my German, and when I switched to English it was clear that he didn't understand my English.
Seriously, if someone talks to you in 'your' language, you can reply in it.
c. Indigenous dwellers laugh at your ability to speak 'their' language
Polish people, unaccustomed to having foreigners learning their language are therefore not used to people making mistakes with their language, and occasionally find mistakes funny. This discourages one from trying to speak the language.
4. They come from an ex-colonial power/country with a lot of power
The sun never went down on the British Empire, as one says. Therefore a lot of people speak English. The US is a pretty important country now (especially culturally), therefore again, English is the language to be used. This has the effect that people in both countries (and in other English speaking countries) are used to the fact that other people speak English, so one doesn't bother learning.
Even in GB, English immigrants to Wales largely don't bother to learn the Welsh language. They assume that 'We live in the same country' (sic.) that all should speak the English language. (I am far from certain where Welsh people are more likely to learn a language other than Welsh or English, saying that).
Russia used to be an Empire and the Russian language dominated the Soviet Union. People from as far afield as the Ukraine and Kazakhstan are likely to have the Russian language in common. This results in the fact that some Russians assume that other countries speak their language (here I mean in the former colonies). I have heard of Russian people coming to Poland not knowing a word of Polish, assuming that Polish people understand Russian, or that the languages are very similar (which they are not).
In each case (though I believe this to be stronger in English speaking countries) one is culturally expected to only speak one language, and that is 'ones' own. One stands out by learning foreign languages. (Man, I am considered to be a language expert in GB, even though I only speak two languages fluently and two languages semi-fluently).
5. Their work doesn't require them to speak the language of the country they live in
I know plenty people from English speaking countries who haven't really learned the language of the countries they now live in. A key factor here is the work they do; they work in English. This also happens with people from non-English speaking countries. They work in some business and English is the dominant language. Unless one is speaking the language every day, it is difficult to learn it properly.
This is one effect of capitalism. The system is such that foreigners can be paid less, and therefore one sees an array of au pairs not needing a high level of the language in question further than that for babies or children; or in factories one can get a load of foreign workers in to do some bog-standard work, pay them little, and not really require them to speak the language of the country in question. Injustice against foreign workers leads of course to prejudice not against those who dominate the system, but those who are victims of it. Capitalism benefits from and increases the issue of the separation of people into 'national' groupings.
6. They are lazy or don't want to learn the language
This can happen. I have heard of some (some, not all) Polish people moving to GB and not bothering with the English language (incidently, I see nothing wrong with people moving to richer countries and working there, even while not learning the language commonly used there; human beings are more than the language they speak). I also know similar stories of British people in Germany and Poland.
Indeed, I also know of elderly British people moving to retire in Spain and not learning more than a very basic Spanish.
(Actually, what are now called 'countries' have largely always been multi-lingual with immigrants continuing to speak their first languages. What is now called GB contained people whose first languages were very diverse. My point being: I do not see it as a matter of fact that immigrant should learn your language.)
Sometimes they don't even need to learn the language. They work and live their daily lives in their first language. They get by without it.
7. They are prejudiced against the language in question
I know this more with the German language. The German language does not have a good reputation; due to the history of Germany in the 20th century, as well as the view shared by many that it is an 'ugly' language. Anyone who has lived in various areas of Germany (say, Bavaria or Brandenburg) would see that the German language can be a beautiful one. Anyway, some people don't bother using their abilities to learn German as a result of this. This may be the case in other countries.
8. They face prejudice and discrimination from people from the country in question
Some Kosovans I knew in Germany complained of prejudice coming their way. In GB some people hold prejudices against people from other countries (even within GB this happens). This has the effect of people associating the language with prejudice and therefore rejecting it.
9. Propaganda about the language in question
People say that their first language is very difficult and hard/impossible to learn. This discourages immigrants. Some immigrants start this propaganda themselves. Add to that any of the other issues here and you have a potent mix for not trying properly.
10. A nice round '10' would be nice, wouldn't it? I can't think of another, however. It's up to you in the comments underneath :)