When an acid (HA) reacts with a base (B), the neutralization reaction is:

The equivalence point is defined that n(HA) = n(B). The explanation for

at equivalence point [without doing any mathematics]
if HA is strong, then its conjugate base A- is neutral
if HA is weak, then its conjugate base A- is weak
if B is strong, then its conjugate acid HB+ is neutral
if B is weak, then its conjugate acid HB+ is weak
Hence, whenever you have a strong vs weak titration, you will end up with a neutral product (conjugate of the strong acid or base) and a mildly acidic/basic product. The pH of the equivalence point is affected by this mildly acidic/basic product.
A mathematical explanation would be more suited to unit 4 when acid/base equilibria is studied.
inb4 anyone asks what will happen when I react weak + weak, the answer is no one does that because it's impractical, but if anyone did, it'll depend on the relative strengths of the acid and base, and it'll be best predicted by computing the equilibrium.