If you look at the PN532 datasheet, you’ll see that it is specified to work only at 13.56MHz and only with several specific tag types.
And in fact, a radio circuit for 13 MHz will not automatically work at 125KHz as the tuning is likely to be quite different. This module was designed to work only at one frequency.
From AN1445 - Antenna desugn guide for MFRC52x, PN51x and PN53x
The symmetry in antenna design is absolutely necessary with respect to tuning and EMC behavior. Otherwise common mode currents are generated to parasitic capacitances from the antenna to ground. Theses currents can cause emissions that hurt EMV regulations
It can be ...
It looks to me like that is the ground return path for the loop. If you'll notice that on the other side of the board the last loop crosses over and the 3rd coil is actually the last coil before ground.
I think the main reason this was done was purely asthetical, as the current through the loop would be the same. It could change the mutual inductance ...