Why does TIA/EIA 568A and TIA/EIA 568B use pins 1, 2, 3 and 6 to send and receive, instead of 1, 2, 3 and 4? Is there a significant reason for this?
I assume you're talking about 10BASE-T and 100BASE-TX on TIA/EIA 586 wiring.
As you can see in this wikipedia article, pins 3 and 6 are in the same twisted-pair, and using a pair is necessary for signal integrity.
An why are pair arranged like that? probably for compatibility with others registered jack connectors.
The reason is: high transmission rate will not be possible if data pairs are close together as they start to interfere with each other.
They create a magnetic field as data flows through at high speed, which means that if 2 high-rate data streams are close to each other, their magnetic field alters the value of data going through, which means packets are dropped which resets the transfer speeds, and instead of being able to have 1Gbit of speed, you get 100mbit of speed.
To understand how this works, you need to understand how an UTP cable works.
UTP stands for Unshielded Twisted Pair, and uses the RJ45 connector at both ends.
As the name UTP already suggests, in order to have a higher speed possible, inside the cable, the smaller cables are twisted in 4 different pairs. The cable itself has no shielding from each other.
Each pair consists of a color: blue, green, orange and brown, where each set has a solid and striped version.
Because the cable is not shielded, if you would simply wire the cable, grouped by color, data transmission channels would run too close from each other and their magnetic field would bleed to the other cable it is twisted with causing to cause interference similarly as how a tv antenna cable can pick up static on its cable if its not properly shielded.
Most of the data gets through, but not all. Because TCP connections check if packets arrive in order to determine the speed, connection speeds will continue to drop after it speeds up causing a speed of 100Mbit to be reached over a cable that could potentially reach 1Gbit.