pH is defined as negative log of H+ concentration in solution. When we mix two solution with different pH, the pH of resulting solution is also calculated by the H+ ion concentration in resulting solution. It is not simply the addition of two volumes.
Let us calculate it.
[H+] for solution with pH = 1 is 10-1 M
[H+] for solution with pH = 7 is 10-7 M
Since, equal volumes of the given solutions are mixed; concentration will be halved.
Therefore,
[H+]= 10-1 + 10-7/2
= 10-1(1 + 10-6)/2
= 1.0 x 10-1/2
= 5.0 x 10-2 M
pH = -log [H+]
= - log [5 x 10-2 M]
= 1.3