T568B was based on old AT&T wiring scheme for their digital PBX phones. Those used Pairs 2 & 3 which were pins 1&2 (pair 2) and pins 3&6 (pair 3). These are the original data pairs (for 10Base-T and AT&T digital phones). Pair 1 stays on the center pins 4&5 so they can be used for POTS as a 4/6 wire RJ11 can plug into the RJ45 outlet. This was the start of LattisNet which evolved into what we now know as ethernet wiring
IBM of course begrudgingly accepted that data wiring was going the UTP route but of course could not use their arch rivals wiring scheme. Their big plan was for everyone to use Token Ring, but the cable and connectors, were horrible and it was next to impossible to actually support any large number of devices. Everybody had to maintain some sort of proprietary system so they could keep all the duckets flowing in. Their data used Pairs 1 & 2 and in many cases tried to stay with RJ11 jacks/plugs. They figured out if they just swapped the Pair 2 & 3 pin outs on an RJ45 from the T568B scheme, and created the T568A scheme. They did a better job lobbying the Feds ($$$) and got it standardized as the scheme to use.
Many of the other systems used basically RS232 which was easy to adapt to telephone style wiring so the T568A worked well because you could stay with 4 wire RJ11s.
Where this only really mattered was if the equipment room used punch blocks (110 for AT&T, 66 Blocks for IBM/Rolm, and of course everyone's favorite BIX block for Northern Telecom). You had to know what pairs to cross connect. Now everything uses patch panels, as long as both ends are the same (A or B), it all works. The wires don't care what color they are, just that they are paired correctly and in the right places.