When someone in your family or friend group enters into a relationship, it can be a testing time for everyone. Not only is this new person about to become a big part of their life (possibly against your wishes), but they're also going to be taking away some of this person's time that used to be spent with you. Whether it's a friend, a sibling, or even a parent- if you're relationship is close, it might be hard to adjust to at first.
Sometimes they're going to choose this significant other over you. And it's not because they are more "significant" than you, it just means they're significant enough to make sacrifices for. They just might not have as much time to give you anymore because now it's being split in another direction. I know what you're thinking - "Well, make time!" Unfortunately, there are only so many hours in a day (and truthfully I don't know anyone whose rubbing elbows enough with Father Time to change that). There is only so much a person can do to balance everything they have going on in addition to this new relationship and you.
Although it might not feel so simple, it really is a simple matter of time. When this person starts dating, it's possible they may only be able to give half the time they used to, or even less on some days. And sure it may feel awful, but that doesn't mean that they don't care or they don't want to spend time with you at all. It just means they want to spend time with the new person in their life too, and the only way to do that is to spend less time with you. And that's just simple math, not an act of disrespect.
The reality is, if you care about this person as much as you think, maybe it's time to stop griping about their lack of time, and start getting a grip. Change is inevitable. This person could be in their life for an indefinite period of time, and the sooner you start to understand their new priorities, the sooner things will start to improve. Taking things personally will only lead to them wanting to spend less time with you because they won't feel supported or understood.
So instead of getting angry, try to be more understanding. Have open conversations about how you feel, but also know that they may not be willing or able to do much about it. The amount of hours that they have in a day will never change, but your attitude can. It's all just a balancing act - and they're most likely doing the best they can, whether you think so or not.