guys, why playing the king is the best move here? i really just dont get it

guys, why playing the king is the best move here? i really just dont get it

https://lichess.org/jofaf4xS/black#24
White's problem is that the natural 13. Ne2 runs into 13... Na5! when there is a nasty fork threatened on b3, and the knight is heading for c4 as well, targeting the weak e3-pawn. 13. Kf2 looks indeed a bit strange, but at least White can answer 13... Na5 with 14. Re1 and give that pawn protection, therefore it is the best continuation (or rather the least of the evils).
https://lichess.org/jofaf4xS/black#24
White's problem is that the natural 13. Ne2 runs into 13... Na5! when there is a nasty fork threatened on b3, and the knight is heading for c4 as well, targeting the weak e3-pawn. 13. Kf2 looks indeed a bit strange, but at least White can answer 13... Na5 with 14. Re1 and give that pawn protection, therefore it is the best continuation (or rather the least of the evils).