Why shouldn't the BATFE release trace data to the public?

Because anti-gun groups have a pathological need to misuse it:

But ATF and gun proponents found flaws in the Brady Center’s calculations.

ATF supervisor Todd Reichert in Washington noted that the agency’s data included some gun sales that were originally made as much as 10 years ago, which is much longer than the two-year “time to crime” ATF considers an indicator of a possible illegal gun sale.

Reichert also said not all law enforcement agencies report recovered crime guns for tracing. And, he said, spikes in the numbers come after ATF help police agencies clear backlogs as those departments begin reporting recovered crime guns to the federal agency.

So even though there's a full page disclaimer on every single report, the Brady's IT guy must have developed a way to have that page show up blank when they review it. Otherwise they're intentionally lying.

I personally like this little bit:

The Brady Center said that number represented 75.8 percent of all guns recovered at Georgia crime scenes.

If they want to use trace data as statistics, then perhaps they should mention California, their #1 state, has the same recovery rate.