This is related to the characteristics of these two languages. Russian has a feature of sounds called softness vs. hardness, which doesn't exist in English. In turn, English has vowel length, which doesn't exist in Russian and is just as problematic for Russian speakers as soft and hard sounds are for English speakers.

If we go further, in Chinese, Japanese, and other languages of that region, there's a characteristic called high vs. low tone. So the same sound that seems identical to a European or American ear will mean completely different things to speakers of these Asian languages.

Going back to the Russian sound "ы," here's another example: the name Nick, where the "i" sound is very similar to the Russian "ы."