rejection = when someone refuses to accept, use or believe someone or something refusal = when someone refuses to do or accept something "Our request for permission to travel met with/received a flat/point-blank (= complete) refusal from the authorities." Cannot really give any other reason than that "a flat refusal" is a phrasal that always goes together.

Decline = a polite refusal There is no flat decline (no matter what decline you are talking about) Refusal to say no Disapproval = To disagree with and look down on at the same time. rejection = to insult while refusing It is true he rejected an offer, but that is not rejection. True "rejection" should come with an insulting feeling. You asked him to do something. When he said no that was him refusing to do what you asked, but where is the insult? If you had not asked him TO DO a specific action, (to join) then a refusal would not be an option. If you instead said something more open ended: the group would like him to consider what part he might play within the group - and he said something negative like- that will not be happening- he will never join such a group - that is rejection.

I tried very hard to persuade him to join our group but I met with a flat refusal