But why in both standards there is one pair that is not adjacent (pin 3 always pairs with pin 6)?
Phone standards traditionally put the first pair on the middle, then the second pair straddling it, then the third pair straddling that and so-on. RJ series connectors were designed so that you could plug a smaller plug into a larger socket and it would end up in the center and this wiring arrangement meant that plugging a smaller plug into a larger socket would result in a sensible connection.
This worked fine at the low frequencies of voice and old low speed data systems but was poor for crosstalk. noise susceptibility, reflections etc at higher frequencies. The greater the number of pairs in this arrangement the worse the high frequency performance gets.
A wiring standard with each pair of wires on a pair of adjacent contacts would be best from a high frequency performance point of view but would be lack any backwards compatibility with the existing telco standards.
The standard used for ethernet is a compromise. The two central pairs are arranged in the same way they would be in a traditional phone wiring giving compatibility with phone applications that only use the first two pairs. The two outer pairs are arranged in a way that optimises their high speed performance.
Once I have got a wrong long cable that was working intermittently. It was made with all rings adjacent to their corresponding tips. After correcting it worked fine.
When doing differential signaling on twisted pairs it is important that a pair of signal connections are actually on a twisted pair of wires. If the two lines from a signal pair are split between two different twisted pairs then this is known as a "split pair" and will have far worse crosstalk and EMC performance than it should have.
Therefore your cable must match the pair arrangement your devices are expecting.
But I am sure that I have already seen a short cable that worked fine too. Hence there must be an effect that this configuration avoids which I have googled and not found.
Signal integrity problems become worse with increasing cable length.