Manipulating Equations: Substracting two equations

Question

I was wondering why I fail to substract two equations using thread, while it works properly, as described here for additions.

Example: Let a system of equations be given:

eq1 = a + b == c
eq2 = a - b == c

I can add both equations (1) + (2) using using Thread:

Thread[eq1 + eq2, Equal]

which gives the correct result:

a == c

However, when I substract the two eqations (1)-(2) via

Thread[eq1 - eq2, Equal] 

I get

a + b - (a - b == c) == c - (a - b == c) 

and simplifying it gives me the first equation.

a + b == c

Can anyone tell me why Thread does not work with a minus sign? Sorry if this is a trivial question.