He proved that males tried to fertilize as many females as possible, but the females were more heavily invested in their offspring and didn't mate as often.
Or did he?
Gowaty, Kim, and Anderson tried to replicate his experiment. Oops. (They didn't completely succeed in a perfect replication: one of the mutant strains Bateman used is no longer available; but still...)
Back in the day Bateman didn't have DNA testing, so he used fruit flies with various easily visible mutations and looked at the offspring. The repeated experiment looked a little more closely at the numbers, and concluded that combined mutations appeared less often than they should have. In addition mothers were identified less often than fathers, which makes no sense. Implication: the numbers were skewed, and it isn't possible to estimate sex selection rates from them.
Other analyses found further problems. For instance he ran 3-4 day studies when males mature in 1 day and females in 4. And it looks as though he made a calculational error, and some of his results aren't significant.
Why did it take 64 years before somebody replicated the experiment? The experiment was tedious and labor intensive. It wasn't an LHC or IceCube size experiment, but it was hard enough to do right to dissuade people.
The good news is that DNA testing can make the test more accurate. It'll still be tedious, though. And a bit pricy: it is more expensive to DNA-analyze a fruit fly than to eyeball it for twisted wings.