Tempted to ask what it is about a taildragger .....
The argument runs that being more difficult to land and handle on the ground becoming proficient in flying a tail dragger enhances your piloting skills... skills which you might not need if you didn't have to handle a tail dragger
They are simpler in construction of undercarriage and less draggy. Many but not all are short field aircraft, (not so a Pitts S2 or an Extra, perhaps) but that is perhaps more a function of wing than landing gear. Modern tricycle gear VLA types are equally short field.
Against them, they are much more of a handfull in cross winds and less stable in landing roll (generalising a bit here). There is nothing really logical in their favour as compared to modern nose wheel types. Nothing at all
Sometimes you can argue yourself into an armchair. I shall just keep flying my Chipmunk (if we ever get the engine repaired)