Once I even tried to go all old skool and got a safety razor that took traditional blades, and some shave soap and a brush. Christ almighty, I thought I was flaying myself alive. It was absolute agony.
There are three possible reasons for that:
1) Your skin might be too dry to use soap. Same happened to me as I thought the skin on my face was peeled off by sand paper after a wet shave. Try avoid soap but instead use some shaving cream.
Solution: Or better still try to apply some cold extract/pressed oil (thin layer) like Olive, Almond, Hemp seed, Jojobar etc to your face and leave it for 3-5 mins. Then apply some shaving cream or soap to start wet shave. After you have finished shaving apply cold water and apply after shave cream / moisturiser whatever you want.
2) Applying too much pressure which you shouldn't.
Solution: Do not press the blade but rather let the blade do the cutting.
3) Angle of holding the safety razor while you shave.
Solution: The one you have might be too aggressive for you so you might want to try some of the adjustable safety razors such as Merkur progress / Gillette fatboy/slim. Merkur Futur can be rather aggressive.
🙂