I have wondered for some time now why I have resisted having my male dog, Mowgli, neutered when I felt no hesitation about having my female dog spayed; I have worried, in fact, that I might be a secret sexist after all. I have considered that my reluctance was due to the fact that his appearance would be changed by the operation while hers would not, or that I secretly like his roaming -- it gives me someone to worry about now that most of my children are grown.

I think of this every year when it comes time to have Mowgli's license renewed. For three years now, the Montgomery County Department of Animal Control has been sending me a bill identifying him as an unspayed female. The reason this matters is that in Montgomery County the license fee for an unspayed female is $20 but for an unneutered male only $6. The computer refuses to understand my letters, my phone calls, my torn-up bills. Though I have written checks, year after year, for $6, they keep sending them back, demanding the full $20.For three years, I have gone without paying and Mowgli has gone without a license.

Still, I consider myself a good taxpayer, and so when the bill came again this year with its same mistake, I determined to try again. Man Against The System . . . er, Woman Against the System. Besides, if I devoted the usual time to a phone conversation with Animal Control, at $6 an hour for my time we would soon be even.

This time I was assured, once again, that the mistake would be corrected. But when I hung up, a new thought occurred to me. Why should the fee for an unspayed female be $14 more than for an unneutered male? It seemed blantantly discriminatory, sexist in the worst way.

I redialed Animal Control. A male voice answered. "Excuse me," I said. "Could you tell me why you charge more to license an unspayed female than an unneutered male?"

There was a momentary pause. I imagined his pointing at the phone and making circular motions beside his head to signal his colleagues that he had a "crazy" on the line. I imagined jokes about women's lib running unleashed in the streets. I almost hung up.

Instead, his voice came back sounding perfectly assured, as though he answered this question every day: "Why yes, ma'm," he answered, "you know there are a lot of unwanted pets out there, sometimes carrying disease, and since the female has the litter, this is one way we try to control the animal population."

"But I still don't understand why it's more important to have females sterilized than males," I said. "The females don't have puppies by themselves," I persisted. I thought I heard him mutter "no kidding?" under his breath. I plunged ahead. "You see, females can only have one or two litters a year, but one male can impregnate a whole neighborhood. Besides, if you charged males $20 you wouldn't have all those male dogs running loose, howling and whining all night." My logic seemed faultless.

"I don't think you understand," he said slowly, with the patient weariness reserved for explaining things to the feeble-minded. "It's like this: Say you have 10 females and one male. That one male could impregnate each of the females; if each of the females were to have a litter of 10 puppies, you'd have 100 puppies!" He finished with a kind of flourish of triumph.

Although my mind begins to fog when someone mentions numbers -- it's known as "female math anxiety" -- I was quick to counter. "Exactly!" I said. "If the one male were neutered then none of the females could have puppies! To have 10 females sterilized instead of one male is sex discrmination!"

"Look, lady," he said, his voice rising in exasperation, "the Constitution does not apply to dogs!"

The conversation seemed to have reached the outside limits of absurdity.

Later, a woman friend pointed out that the man had a point. "The thing is," she said, "the county can never get full compliance with those regulations, and one unneutered male could produce dozens of litters. The more unspayed females you have, the more litters you'll have."

"I suppose so," I said, "but it still doesn't seem fair. If all unsterilized dogs were charged more, we'd have even fewer unwanted puppies."

"Well," my friend answered, "life, my mother used to say, isn't fair. Consider this: Who spent all those years trying to straighten this out? You did, right? And if your female dog had puppies, who do you think would have to take care of them, find homes for them?"

I remembered the man's parting words: "The Constitution does not apply to dogs?" It has occurred to me that in matters of sex discrimination, the Constitution does not apply to women yet, either.

Mowgli, my pet, move over!