Why XOR can be a symmetric encryption and decryption?

Why does Bluetooth security use XOR as an operation of symmetric encryption and decryption? The formula of symmetric as follows.

C = Enc (P, K)
P = Dec (C, K)

Where
C is cypher text.
P is plain text.
Enc is a symmetric encryption algorithm.
Dec is a symmetric decryption algorithm
K is a key of the encryption and decryption.

The true table of XOR is as follows.

A B X
-----
0 0 0
0 1 1
1 0 1
1 1 0

A XOR B = C
C XOR B = (A XOR B) XOR B =  A XOR (B XOR B) = A XOR 0 = A

Therefore we got the formula.
A XOR B = C
C XOR B = A

Lets rename A to P (plain text), and B to K (key), and keep C (cipher).
P XOR K = C
C XOR K = P

Transform it.
C = XOR (P, K)
P = XOR (C, K)

We proof that XOR can be a symmetric encryption and decryption.

-Count