Why does an increase in money cause a proportionate increase in price level according to classical/neoclassical economists?
It's a bit hard to answer without a precise model structure, but normally an increase in money will propagate into an increase in nominal demand. For the sake of simplicity, suppose money is equivalent to nominal gdp $M$, whereas real gdp by definition is given by $Y=M/P$. In classical economics, real gdp is pinned down completely by fundamentals of the economy, so that accordingly $P\propto M$ (namely by a factor $1/Y$).