So the hole in the wood cabinet is too big? Glue some toothpicks or a matchstick in it and then rescrew

@HALLETT & Co. I am unable to understand if the hole is too big. If I screw it in without the hinge, it goes fine and is taut but when I use hinge and screw it in, it does not go all the way in. Am I not screwing it in at 90 degrees?

You can get wood round stock the diameter of the hole, push it in as far as you can, mark the needed length, cut and install with wood glue. You then drill a small pilot hole and install screw securely. We did this on some loose cabinet hinges and it worked great.

From the pic, it looks like they might be local shop made cabinets? Are the frames on your kitchen cabinets made from pine ? Post more pics of the cabinet doors. That could be part of the problem...the soft wood frames. I hope all your hinge screws don't start to strip out. Do you know how old the cabinets are? They don't look that old yet. Maybe post a picture of the kitchen farther back.

@The Kitchen Place thank you! below is a picture of the cabinet doors.

how can i find if they are pine and custom/local shop built?

I believe they are at least 20 years old. I did notice that one other cabinet door was also almost in similar if not worse shape as this one.

what do you suggest in the long run as a solution?

Either fill the hole with toothpick, matchstick, bamboo skewer, etc. & glue as already suggested or get a size larger and longer screw. Or both.

Another trick is to use a small length of bare solid copper wire (from Romex/ house wiring). Place the snippet of wire in the hole and then drive the screw.

Toothpick and glue will get you twenty more years.