You are asking questions of deeper psychological significance than we can answer outside of guessing. Most of the answers about your fwb lie in his past. By his past I am speaking of his early relationships with women from his mother and even his first love. Sometimes trauma in these relationships can affect men’s actions later in life.
Your fwb seems to have an obsession- hate- (or ambivalent) relationship with the girl. All the why, why, why’s you ask most likely can only be completely discovered through deep talk therapy and perhaps regression hypnotism to uncover the real mystery of his actions towards women.
In a nutshell it seems he doesn’t know how to love, be intimate or be committed. Perhaps a prior trauma makes him avoid these feelings at all costs? Since you and he apparently do not have long intimate talks about feelings, life etc, it is likely you will never know and simply be a pawn in his life’s drama.
The girl isn’t following his expectations. She is nice but not sexually available. She keeps him at an arms length sexually. This utterly fascinated him. She seemingly is manipulating the Manipulator! Why does she bother? Well another paradox of human psychology!
You could spend your entire life in this toxic relationship and never have any more answers than you do now. We not being a fly on the wall during a hypothetical psychological counseling session can only guess based on what you tell us which is obvious superficial.
She definitely seems to not be interested in being his beck and call girl. She approaches him from a position of control,self confidence and not total submission. She is not likely to allow herself to be totally used by him. He finds that interesting to say the least.
As far as his disdain/ hate for her. When he doesn’t get what he wants , when he wants it he is the upset immature boy child. More questions, I am sure, but not being psychologists, we can only guess. You have experienced some of this when he doesn’t reply to your text for a period of time. He is unstable, and runs the gamut in emotions.
The “why” of why doesn’t he tell her about him and you seems obvious. He doesn’t want to blow any chances with her! The “why” of why doesn’t he respond to her text, is a very immature petulant reaction to her disappointing him. He seems to expect women all women to be subordinate to him, when that doesn’t follow through he is temporarily peeved. That is until he sees her in person. Then his lust seems to take over. He mostly likely isn’t a happy camper most of the time. This must not upset you all that much him being “moody” as you proceed to have sex with him.
This cycle repeats with him over and over and is quite predictable.
The question being will he ever tell her to f- off? Will you ever tell him to f-off. So far the answer is no. If I am right we can expect this story to be the same throughout 2022 and 2023.