Why does my Kennedy half dollar have no mint mark?

If your half dollar is between the years of 1965-1967 then it would not have a mint mark. Mint marks were suspended on all coins minted those years due to the changeover from silver to clad coinage.

If it is not within those years, coins from Denver are be marked with a D and those from Philadelphia either have no mint mark (up to 1979) or a P (1980 to the present)