We're social creatures and we love little more than feeling validated by a fellow human. It's easy to get caught up in such thoughts. I think it's important to realise it as just that . A thought. A transient experience which only exists as long as you hold on to it.

Does 'x' dislike you because they neglected to wish you goodbye. Probably not. People don't generally happily talk to another for ages if they feel disdain towards them. And if they in fact do? Then the whole thing is essentially inconsequential. You only stress yourself out and cause anxiety by pursuing such thoughts. Consider the person who didn't reply for a day. Really think about all the circumstances that could've arisen within their life which led them not to be able to respond. With those in mind, is torturing yourself with your original, singular outlook worthwhile? Trying to step out your own perspective can be good when dealing with such things.

My uninformed conclusion is that you're getting caught up with such things because you feel your opportunities for social interaction to be few. In turn, you over analyse any behavior or cues from the chances you do get. I think it's also important to consider the effect of these thoughts on your future interactions. You already stated that you only talk to people that approach you first. This is very limiting. I know from experience. I recently spent 6 months in a different city and had 0 of my own friends the whole time. Why? Because I made no effort myself. The one time I developed any sort of relationship was when I made the effort and went to a reddit meetup with a load of complete strangers. I met some cool people but failed to capitalise on that, even when they reached out to me in the future. You can't always expect things to come to you without any action on your part, and then be upset when nothing happens.

On a final note. If you feel the being home schooled is hurting your social development, then it's important to air that to your family. A prime reason for homeschooling in the first place is because they want what they think best. They would hopefully be concerned to hear you feel this way and make efforts to amend. I know this is somewhat of a jumbled response, but I hope it was a worthwhile read. :)