Are you removing the connection because it started to leak? You didn't mention what this connection is for. It it's a water heater nipple, those nipples are steel and can tear up a thinner washer such as used for spigots and washing machine hoses.
Since this is your second time, it is possible your are over tightening the connection. Tighten down the nut until you feel it bottom out when using a wrench. A tad more than finger tight. Then turn it no more than 1/4 to 1/2 turn. Turn on the water and check for leaks. If there is a little weep of water tighten the nut ever so slightly.
These washers are that flat and large to seal the nut and the flex pipe since there is no compression ring. You can try other washers types.
The washers are neoprene and is fairly tough material. To me they are being torn apart because as you tighten down on the nut, it is tearing the washer. If you have silicone grease, coat the washer with it so it acts like a lubricant. This will allow the nut to slide over the washer, thereby preventing it from being damaged.