Suppose I moved back in time so that the breakfast is still there...

Then you would meet your earlier self and you would need to fight for the breakfast.

But I didn't fight when I had it in the first place.

You would have, had you later travelled back in time.

I would go back in time only if I had the breakfast...

...but that means I would lose the fight for it later!

Yes. The law of conservation of breakfast is merciless.