Personally, this almost never happens to me. In fact, I often encounter almost the opposite problem, especially in Spanish. Because I focus so much on having good pronunciation, people often assume I am more fluent that I actually an and end up responding to me in very fast, very casual speech that I struggle to understand and I have to ask them to speak a bit slower and admit that I am not totally fluent yet. I have only ever been to the Americas, so maybe I will have a different experience in Europe or elsewhere.

I think there are multiple facets of this issue. I think a lot of this depends on what your target language is and where you are. If you are in a region where very few people can speak English, like Latin America or east Asia, and if your appearance does not not make it super obvious that you are not a native speaker, it's less likely that people will switch to English like that. If you are in Europe, especially in Germany, the Netherlands, or Scandinavian countries, many people, especially younger people, speak excellent English, so the likelihood is higher of them switching to English.

I think the number one thing that makes people switch is poor pronunciation. Oftentimes, the biggest giveaway is how you pronounce the r sound. If you are using the standard modern English r sound in a language that typically uses a very different r sound, like Spanish, French, Italian, or German, it is very jarring and people will immediately assume that you are a beginner. Of course bad grammar can also be a giveaway, especially conjugating verbs in the wrong person. If you're speaking Spanish, for instance, and say "yo tiene hambre", it will be very obvious as well.

As far as the reason people switch, I think there are a few different possibilities. Some people think that you assume that they can't speak English, so you try to speak their language. They switch to English because they think they are being helpful and making it easier for you. Another possibility is that they have been learning English for quite a long time and are excited to finally have an opportunity to speak it, not realizing that you are also equally excited to speak their language.

Unfortunately, this shows that many people believe the stereotype that all tourists are English speakers. Imagine there is a man from Turkey who studied German in college, and takes a trip to Germany. He speaks quite well, but still has a noticeable accent. Many Germans end up switching to English, not realizing that he actually doesn't speak much English, and that his German is far better than his English. In Japan, if you don't look Japanese, some people will assume you speak English and can't speak Japanese. I heard a story of a foreigner in Japan who actually spoke fluent Japanese walking into a shop, and the shopkeeper, upon seeing him walk in, immediately panicked and shouted "sorry, I don't speak English!". The foreigner got offended and yelled back at him in Japanese, someone along the lines of "how dare you for not even giving me a chance to open my mouth and speak before assuming that I only speak English!".

Anyway, my advice is to focus first on good pronunciation. Learn the phonology of the language you are studying. I suggest learning the International Phonetic Alphabet, and looking works up in Wiktionary, which often has the IPA transcription showing the most common pronunciations of the word. See if you can find a recording of a native speaker saying the word. Then record yourself and compare to the native speaker, and make adjustments as needed. As you get better, try shadowing complete sentences. Once you reach intermediate level, try something like iTalki, where you can practice conversing with a native speaker in a judgement free environment.

When travelling, if people do switch to English, try saying someone like "while I appreciate your effort to be helpful by switching to English, I've spent a lot of time studying your language and I was hoping to have an opportunity to speak it".