The reason post-money matters more than pre-money for an investor is that it sets your ownership directly. If the post-money is $10M and you put in $100,000, you own exactly 1% — your check divided by the post-money valuation. That simple relationship is why post-money is the number to anchor on: it tells you what slice of the company your money buys, before any future dilution.
The arithmetic is straightforward but the negotiation is everything. Pre-money plus new investment equals post-money, so on the same $2M raise, an $8M pre-money (20% sold) is a very different deal for founders than a $4M pre-money (33% sold). Post-money SAFEs, now the YC standard, are popular precisely because they pin down the investor's ownership percentage at signing rather than leaving it to be recalculated when the round prices. Just remember that the 1% you buy today gets diluted as the company raises more rounds — your ownership at exit is what ultimately drives your return.