Why can't circuit breakers close across a large phase angle difference?
Short answer here.
If you imagine connecting two DC sources like batteries together that have different voltages, you would end up with current flowing from the high voltage source to the lower source. So in the circuit the result is current flow in an undesired direction (short) and in some cases a large current spike.
Now imagine the same example in a power system where you are connecting two AC generators (or breakers to match your question). Remember that in a three phase AC waveform, if the two waveforms you want to sync have a different phase angle, this means that at that instance of time, the voltage magnitude is in fact different, identical to the DC scenario provided above. So if the phase angles of the AC sources were not equal, you would end up with undesired circulating currents between the breakers. Now with the power system the result is a bit more drastic.

Huge currents from the high voltage ranges can flow.
As mentioned in the comments by Andy and Brian above, these high currents cause substantial wear and damage to switch gear, and the magnetic mechanical force stresses placed on rotating machines (generators) is not ideal.

When the two sources to be synced are identical (or very close), the synchronizing will appear transient free.
If you are still unsure and this response doesn't answer your question, I would recommend reading up on synchronizing AC generators and it should provide clarity.