Why a master's mate was an assistant in training

What did "mate" mean in historical naval rank and trade titles?

It meant an assistant or trainee working under a warranted master, carpenter, boatswain, or other specialist.

A boatswain's, master's, or carpenter's mate assisted the warranted professional and learned the trade under that person's authority. The mate could direct assigned work as part of the specialist's team but did not yet hold an independent warrant. Their authority flowed through the warrant and responsibility of the senior specialist. Time served in that role prepared a candidate to qualify in their own right.