Is it safe and how to convince parents

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Where do you live now?

United States

Well some places in the US can hardly be called safe. If you're worried about getting killed then the homicide rate in Ukraine is about 5 per 100,000. Compared to 91 per 100,000 in Honduras I'd say you could do worse (4 per 100,000 in the US). Apart from that it's just a question of being smart. Don't wander around at night especially if you are drunk, keep your money under the soles of your shoes, in your socks, in a money belt or better yet don't carry large sums of money. I don't know what the mugging rate is over there but always keep a bit of cash just in case you do get mugged. Not having anything to give the mugger can be dangerous, especially at knife or gunpoint. Apart from that, you just gotta take your chances. Consider how well you know this Ukranian guy and stick with him. He knows what not to do and where not to go and so if you trust his judgement you should be fine. Just tell your parents you want to see the world and learn more about other cultures outside of the US and how Ukraine is a good choice because you know someone from there who you can stay with.

EDIT: In most metropolitan areas, even in dangerous countries, it is usually safe to walk around in daylight. As long as there are people around you should be good (usually).