This reminds me of a story that one of my English teachers told me. Her parents are from Korea and she told us that once in college one of her classmates starting talking to her in Chinese. She could only understand "Ni hao" and guessed this guy was speaking Chinese. So, she had to tell him "Hi. I was born in Philadelphia and my parents are from Korea. I'm sorry I don't speak Chinese". 

Interesting question!

One thing that could perhaps offend them is that they might feel that you think that their English is not good enough to communicate with, and that you are being impatient with their imperfect English.  I have heard of a number of English speakers traveling to other countries that said that they felt the people of that country were very impatient with them when they tried to speak the local language, and instead switched to English.

Also new immigrants might feel that they stick out as a foreigner rather than a local, and that you count them as a stranger rather than as a member of your community...  If they are trying to integrate they might feel hurt.

Other immigrants instead are delighted as they feel loved and welcomed when you speak with them in their language.

As others have mentioned above, it could also very well be that their goal in traveling abroad was to sharpen their English, and they may feel that their goal is not being met.

Personally I don't think it should be offensive.  It shows an interest in them, and it should be counted as a great honour that you have taken the time in your life to learn their language!!  I think most people would be very thrilled to hear someone speaking their language with them!!  : )

I would say it depends on the context. I am a native Chinese speaker and I have been studying and living in America and Europe for several years. I have always been happy to speak to a foreign student when he/she started a conversation in Chinese with me. Typically they were willing to learn some/more Chinese and interested in the Chinese culture, which usually created a sense of connection for me.

Yet sometimes I encounter random people on the street and they yell random Chinese (or Japanese) phrases to me…and that’s when I would definitely feel offended.

With that said, many of my American friends have had the experience of getting frustrated when they were studying abroad in a non-English speaking country and the locals talked to them only in English, because it made it harder for them to practice the foreign language that they wanted to learn.

Hi 

Depends on the context but as a English speaker if I am abroad to learn the language of the country where I am and people kept speaking to me in English it would really annoy me. So if these Spanish/Mandarin speakers etc are in America to learn English having paid their money to fly there/live there and generally immerse themselves in the culture I can understand the frustration when they do all that only to have someone respond in their native tongue! Of course if you want to practice with these people the best way is to arrange a exchange.

However saying that I was recently in a very touristy part of London where I got talking to an Italian couple, out of respect I spoke in English as we were in London and I assumed they wanted to practice. But I also mentioned in passing that I was studying Italian and they happily switched to Italian themselves as they were both struggling in English and were relieved that I could help them. So I guess it depends and I would always check to make sure the person was ok before switching languages.

It depends on the context and the tone of the conversation. Sometimes English speakers sound as if they meant they assumed that one does not understand English or don't know any English, so yes, that sounds offensive. And it makes it worse if they even speak slowly to you in Spanish.    It depends on the tone, if they want to be friendly people will notice it, if they want to be condescending because you are a foreigner and start making assumptions about your English skills because they draw conclusions about your foreign appeareance that sounds rude to many people.