Why do you feel shy being around girls/boys that you 'like' and why do you feel embarrassed to ask them out?

So shyness usually happens when you are talking to someone you find inferior to and therefore your brain uses this mechanism, shyness, in order to protect you. For some reason, your brain sees this person you feel inferior to as a threat and by being shy, it's trying to make you pull away from this person. When you like someone, you probably find them attractive and to some extent, you feel like they're out of your league and therefore you are in a sense inferior to them. Because you see them as someone who is superior to you because they are attractive, you become shy so that you avoid this person because your brain is telling you that he or she is a threat when in reality they're usually not.

So about your embarrassed question: Embarrassment is thought to have evolved because it is actually a good thing. Yes it can hinder you from being bold about asking someone out but research shows that people who display embarrassment towards others shows them that they are trustworthy, humble, modest, and more generous. It is a sign of virtue and shouldn't be something to dislike. So when you're trying to ask someone out, you feel embarrassed most likely because you are trying to show the person you're asking out that you are a good person, that you are modest and trustworthy. Now remember, don't confuse embarrassment with shame because they are different things. Shame is something deeper and it's typically stemmed from guilt.

So that's just my explanation of it. If you don't believe me, feel free to look things up on your own because there are some really interesting psychology articles and blogs about this. Even VSauce, the YouTube channel, did a little thing about embarrassment in his video "Why Do We Wear Clothes?". Hope this helps.