Why Does Neutering Dogs Screw Their Minds Up?

AS a responsible dog owner, I encourage people to have their pets neutered…I can’t stnd the thought of allof those unwanted puppies being euthanized. But, a question: my neutered English Springer Spaniel (male) pees like a female! And, a spayed female doq we are fostering acts like a male-she lifts her leg like a male dog, and sometimes tries to mount other dogs!
What is it that screws their sex hormones up? Does the removal of their sex organs result in a semi-genderless state?

Minds = sex hormones?
Sex hormones = minds?

Our male dog pees like a female, sorta. He doesn’t lift his leg. The vet told us that if you get him fixed before he starts the leg lifting habit then he probably won’t ever lift it but he didn’t say why. I’ve known other dogs who have been fixed after they started leg lifting, and continued to do so after being fixed.

Our female dog still pees the same way she did prior to getting fixed.

Aside from some apparently minor discomfort for a very short time, none of my dogs (male or female) ever changed their behavior as a result of being fixed.

Our dog does both. If he’s in the mood he’ll lift to pee, if not, he’ll squat. We got him after he had already been ‘taken care of’ so I don’t know what he was like before hand.