Sorry followed by “but” is a rebuttal in disguise.

An apology with a justification stapled to it is an argument for the defence, and the second half is what the other person hears. The word but cancels everything in front of it, which is why it often lands worse than saying nothing. Your reasons may be entirely valid. They simply belong to a different conversation, later on.

Say the apology and stop when it ends. If the context genuinely needs explaining, ask afterward whether they want to hear it. Most of the time the shorter version does more work.