options - What is the economic reason for the equality in value of an American call and European call?

In a previous question this question came up.

In my mind, if I'm holding an option at time t, then there are possible future price paths where at t+k the option will be ITM but at T the option will be out of the money. Thus, I'd expect the value of an American call at time t to be higher than the European call. Apperently this is not the case, I found this reference that explains it in math, but LocalVolatility says there is a simple economic reason that I am missing. What is it ?