pattern matching - Why rule does not work if Flat attribute?

The following works:

In[39]:= ClearAttributes[M, Flat];
Replace[M[F1[a]], M[x_F1] | M[x_F2] -> x]
Replace[M[F2[a]], M[x_F1] | M[x_F2] -> x]
Replace[M[F3[a]], M[x_F1] | M[x_F2] -> x]

Out[40]= F1[a]


Out[41]= F2[a]

Out[42]= M[F3[a]]

the following does not

In[34]:= ClearAttributes[M, Flat];
SetAttributes[M, {Flat}];
Replace[M[F1[a]], M[x_F1] | M[x_F2] -> x]
Replace[M[F2[a]], M[x_F1] | M[x_F2] -> x]

Replace[M[F3[a]], M[x_F1] | M[x_F2] -> x]

Out[36]= M[F1[a]]

Out[37]= M[F2[a]]

Out[38]= M[F3[a]]

why?