I'm one that came to DE shaving after 20+ years of enduring shaving and thinking I had the world's most sensitive skin (only thing that caused me more irritation than shaving was not shaving so I shaved about 1-2x per week) coming out in a rash whether I used a single blade, twins, 3 blades, even electric!... Using foam, gel, the whole gamut. I had countless GP & dermatologist consultations that lead to (useless) advice and (useless) drugs... Use aftershave, don't use aftershave, use balm, use splash, wash before, wash after, use soap, use teen acne wash, moisturise, don't moisturise,... All of the usual guff. None of it worked.
A chance hearing of an aside from a DJ on the radio piqued my interest when he said he'd just bought a razor like his grandad's... Thought it was worth a go. Bought a DE razor, some random blades, a random brush and a random soap.
Day 1 was amazing. Close shave, no irritation. Resolved to do it again the next day. Even better. Binned all of the disposable/system stuff. Chance encounter with the (bearded) doc after a week (in the pub) "whoa! What happened to your face?" So the difference was visibly obvious to him... Told him and within a week, he was clean shaven and completely converted.
Have I found anything I am actually sensitive to? Nothing at all (at least nothing I didn't know about before - which is pretty much all fish & shellfish) - Other than an intense dislike of sandalwood - and that I break out if I use a balm/moisturiser.
As others have said pressure (or rather the lack of it) is key if you think you're pressing on too hard, you are. Think of your head as an over-inflated balloon. You are trying to remove the lather from that balloon without popping it.
One last thought: I was stood in a chemist shop when a "demo dolly" sidled up, handed me a plastic more-blades-than-you--can-count doofer and said "this will shave your face closer than any other razor". First thought was "does she have first hand experience?" but I recovered to say "feel my face, I shaved yesterday with a 60 year old razor - I suspect I have less stubble than you"

She groped my chin and agreed...
Then the missus rolled around the corner and I could have been in hot water had she not encouraged her mate to grope me similarly (chin/face) in the street a couple of days before to demonstrate the smoothness of it.