The TPP (and other trade agreements) is largely about establishing key US companies into foreign markets. The US can, unsurprisingly, command the upper-hand in most negotiations due to our massive economic influence. These laws include protections for IP rights, financial regulation, and food/drug safety standards that allow US companies to operate and establish dominance in foreign markets.
If the US refuses to build trade relations, or becomes known for breaking agreements, then that gives China the opportunity to come in and instead establish their entertainment, technology, banking, and consumer goods companies. This would be clearly at the expense of the US and would gradually erode our economic influence around the world.
People around the world drink Coke, eat McDonalds, search on Google, get loans from Wells Fargo, buy stuff on their Visas, etc, largely due to these agreements. This money funnels back to the US to pay salaries, taxes and dividends.
So, short-term, US sheep farmers benefit from not having to compete on fair terms with New Zealand wool. But long-term, all other Americans lose as the income streams from established American companies are transferred to their non-US counterparts.