In a perfectly efficient market with perfect information there's no profit to be made. So to make money you either have to be more efficient - either by market-making where you do millions of small trades, or the kind of value investing where you just buy what other people are selling and vice versa and hold them for a while - or you have better information. (Which doesn't have to mean inside information. It's certainly possible to make a living out of good old-fashioned detective work based on public information - recent clever tricks have been e.g. tracking the tail numbers of CEOs' private planes to know when they're on holiday and/or negotiating a merger).
A perfect market, which is a stupid assumption, can indeed make profit. You are assuming that an economy is a zero sum game but it is not. Transactions are made because both parties come out ahead.
In a perfect market middlemen (i.e. traders) would make no profit - participants already have perfect information and there are enough buyers and sellers for all goods, so people trade directly and would get no value from intermediaries.
This assumes (quite wrongly) that the same goods have the same utility across the population. It's similar to saying, in a perfectly efficient economy, there would be no trades. There are, because there is a benefit to that trade -- and there is no reason for that benefit to be evenly distributed.
