I think OP is confusing "being willing" with the modal would (used to reference a hypothetical situation).
1: I can't think why he will have said that it was my fault <=== INVALID
2: I can't think why he was willing to accuse me
3: I can't think why he would have been willing to accuse me
4: I can't think why he would be willing to accuse me
Note that both #3 and #4 can be used to mean exactly the same as #2, but #4 can also be used to refer to a possible future accusation1...
3a: I can't think why he would have been willing to accuse me in court yesterday
4a: I can't think why he would be willing to accuse me in court tomorrow
Also note that he might be forced to unwillingly accuse me, so we might not want to mention "willingness" at all...
3b: I can't think why he would have accused me in court yesterday
4b: I can't think why he would accuse me in court tomorrow
Note that 3b above would often imply that he didn't accuse me, but it can also be used even if he did accuse me - OR if I don't actually know whether he accused me or not (same as with 4b, where I can't know for certain whether he will or won't accuse me tomorrow).
1 Note that #4 (without "tomorrow") could also be used as a "timeless" reference to the possibility of him accusing me in the past OR the future (or indeed, in any hypothetical scenario unrelated to past / present / future).