He backed down because he wasn't your traditional killer. Out of hatred for criminals and determination to get a criminal convicted, he became desperate and took matters in his own hands. You ultimately discover that Gant is really good at planning things out in advance, but not quite as good when he's cornered and impulsive. He was able to cover up Neil's murder very well, but not Goodman's, which was done impulsively. When Lana started testifying about the SL-9 incident, Gant got scared and wound up revealing critical details in a dire attempt to get Ema convicted, that wound up proving he was the real killer as both Phoenix and Edgeworth backed him into a corner. At that point, Gant basically admitted that the law was going to be in good hands with the efforts of both Phoenix and Edgeworth. If they could find him out with all the effort he went through to cover his crimes up, they could uncover any criminal.
I don't disagree with that, but it's more about how he was built up as this cold badass, but the second you take him down, he kind of just apologizes and laughs about it. I felt like he was built up as calculating and tough with a happy-go-lucky exterior, but the second he finishes breaking down, he starts apologizing and being goofy. It just totally took a lot of the edge away from him as a villain for me, and made him feel more silly than cool. I just couldn't take him as seriously after that portion.
I get his motives and where he made mistakes, and I like those elements, but it's more about him switching gears so quickly and just kind of becoming a wimp at the end. As ACIII said, Redd White would be a solid comparison in terms of just seeming imposing but then turning into a joke, though it wasn't as big of a deal in Redd's case since he always seemed to be pretty goofy. The way the case ended for Gant just made it super hard to take him seriously on subsequent playthroughs.
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