Because they can....

They do it because they can, because you put up with it. There are several possibilities. This allows him to say to the other person "I don't love her. I even tell her I like you." Or it allows him to feel superior; if this is true he has his own problems. Or, he simply has no respect for you. If he did, he would not disrespect you by indicating he has feelings for someone else. Or, he is telling you the truth. He is just not that into you, but he wants to keep you around because you are convenient. Or, he would like to include this other person in a threesome and he is feeling you out.

When you begin supporting yourself, and treating yourself like the queen you are, other people will begin to support you. You decide who you let into your life and if you are looking for encouraging supportive people, you have not found it in this person.

Please excuse my use of the personal pronoun "he" and substitute what makes sense to you.

If it were me, I would say to this person directly, "What's up with the disrespect? Am I misreading that we are romantically involved? Am I misreading that we are exclusive?" If he does not give you a direct answer with an apology, look for someone who CAN show you respect. Without that, there is no basis for a relationship.