Why shouldn't I write "start to" or "begin to"?

Using "start to" or "begin to" plus a verb adds unnecessary words to your sentence. Consider deleting or rewriting for clarity.
Original: Jake started to throw the apple core in the trash.
Rewrite: Jake threw the apple core in the trash.
Original: Mary began to see her opinion didn't matter.
Rewrite: Mary saw her opinion didn't matter.