24 Pin Connector won't secure. Please Help!

Disconnect the cable and inspect both to see if either might have something wedged in it which might be preventing the connector from going in all the way. Double-check that keyed pins are lined up and attempt re-connecting.

If the insertion resistance is fairly even across the whole connector, it is possible that the connections really are that tight. If you are 100% certain your connector is lined up properly and free of any debris that may be hindering your connection attempts and are genuinely concerned about breaking your board by pushing too hard, you have three options: 1) swap out the PSU, 2) use a power cable extension or 3) take the motherboard out so you can attempt plugging the cable with full support behind the connector to avoid bending the board.

Personally, the part that most often scares me is inserting DIMMs since some motherboards have very tight slots that require an absurdly high amount of force to insert DIMMs the first few times.