Capn Bloggs is right on. The first post made it obvious they had no clue how to go from autopilot to hand flying with no experience in hand flying an aircraft so they botched it and didn't just stay in the green area of an RA but put the aircraft in a negative G totally unnecesary dive.
The distance and altitude between them wasn't critical. 1.6 miles and 400 feet is not a near miss.
We did these maneuvers all the time in training and they are smooth pitch changes to stay in the green arc. If you never fly without an autopilot at altitude this might cause abrupt maneuvers. Spirit requires an RA alert to turn off autopilot, FD, AT and stay in the green arc.
I understand the Spirit pilots are encouraged to turn the autopilot on shortly after take off and leave it on until final approach.
We old guys don't agree with autopilot reliance because as has been seen recently AF and now Spirit has shown what autopilot reliance does to pilots flying skills.
Just let these pilots handfly so they don't do this any more. If your checklist says autopilot off then that means the pilot can hand fly. He can't if his company doesn't allow it.