You should be able to lay it on top of the connector and just push downwards. If you’re unable to do so, take out the motherboard again and retry it outside of the confined space of the MacMini, so you can see what’s happening.
Usually, when disconnecting the connector from the terminal, you should be able to pull the connector upward from the side where the wires are coming out of the connector, as simply as raising the wires with something like a thin pointy spudger. That movement should be reversible.