Also: do not attempt to bend the pins upwards to install, and then bend it back. I broke 3 pins that way.
It easier if you unhook the wires from a couple of tabs on the side attached to the case. That allows more leeway to manipulate the connector. There are two plastic tabs, and the wires are routed between them so that they do not move out of place.
I suggest taking a good close-up photo so you can see how the parts fit together. That's how I was able to figure out what I was doing wrong.
Agree with all the previous: this step is not necessary to remove the second drive (the one closer to the bottom of the case. The connector is VERY delicate.
The pins connect into the edge of the connector, not the top or the bottom. So, you should pull it out parallel to the logic board in the direction of the wires, towards the front of the case.
When reassembling, it's easier to connect this before pushing the logic board in all the way.
Need a picture of the socket, after the battery cable has been lifted so we can see what it's supposed to look like.