I apologise for what I said about you?

apologise 是你道歉的动作
for 是表示你上面那个动作的指向
what I said about you是指向的目标

所以这里的for和 what 不是连在一起表示 why 的意思，不能替换。
如果你不理解，可以背下面的公式
I apologise.
I apologise for sth to sb.

为什么事情道歉，介词要用for

下面是几个原汁原味的例句：
It's quite a thing for me to apologise for anything.

We apologise for both errors.

We apologise for the error.

We apologise for any inconvenience caused.

Unfortunately we did not make this clear and we would like to apologise for any embarrassment caused.

Angry Vera replied: `;Why should I apologise for helping charity?

We apologise for our error.

When they had all finished the coffee, Bob got up to pay the bill, leaving John to apologise for his misplaced piece of mockery.

这里for what 不能用why代替

I must apologize for not being able to meet you.
我因为没能接你而向你道歉.
"I phoned Dietmar personally to apologise to him.
“我已经打电话给哈曼向他道歉