We all know panzer iv lasted longer as a battle tank than the panzer iii, mainly because it had a somewhat larger turret ring and so could accommodate the 75mm/42 gun needed to establish some degree of parity with the t-34 in Russia.

But my question is why did the Germans feel the need to develop the panzer iv in the first place? We know panzer iv is suppose to be the support tank armed with an explosive shell firing 75mm short gun to provide anti-antitank gun, anti-fortification and anti-infantry support to the panzer iii. But panzer iii and panzer iv were pretty close in size and weight, and we know the panzer iii could accommodate the original short 75mm gun intended for the panzer iv. So why develop the logistic headache of the a separate panzer iv in the first place?

You kind of answer your own question. The PzIV was initially designed as an infantry support vehicle, hence the short low velocity 75mm gun. It was only after encountering the T-34 that steps were taken to up gun the PzIV with the long barrel high velocity 75mm gun. At about the same time the PzIV was also up armored with additional armor, initially bolt on, on the front hull and across the drivers station.

The short answer would be, room for growth. The Panzer III was only armed with a 37 mm gun to start with, but the design had enough flexibility that it was upgunned three times before the design was maxed out. Had the Panzer III been built with both 37 mm antitank weapons and 75 mm support howitzers at the outset, skipping the Panzer IV, the Germans would have had to develop a new medium tank from scratch in 1941 (which they ultimately did at mid-war, with the Panther, which turned out to be a maintenance nightmare as the newly developed components failed constantly in service).

And the Panzer III and IV tanks in their earliest incarnations, had excellent power to weight ratios and good reliability. Loading the lighter tank with heavier armor and firepower eventually eroded both those qualities.