But corporations are people. Why can't I pay income taxes on my net rather than gross?
Because that's what corporations bought with their "campaign contributions".
To be fair, there are some businesses that simply could not work at all — any kind of deposit-taking institution, such as a credit union or bank, even if not operated by Wall Street — if every piece of money that crosses the doors was taxed as income. Furthermore, there is a general benefit with having companies generally economically active rather than leaving money sitting there doing nothing: taxing net income after allowable outgoings is reasonable. The real problem is that someone found a way (well, several ways) to make income that should be taxed be actually untaxed, and a number of corporations have been using these tricks on a colossal scale. When tax income is generally well up, that's not seen by governments as too big a problem, but when tax income is down, the order comes down from on high to make sure that those who should owe actually pay up. The screaming as the true bills start to be charged will be very loud and shrill indeed.
Ordinary citizens aren't allowed to claim only net income because that would make overall tax income too low; a majority of people have net incomes so low that the taxes levied would be more expensive to collect than what would be earned. It would also make it far easier for the rich to dodge taxes, given that avoidance techniques are now well advanced. (Right now, they have to do games with corporations and loans and tricks like that.) I fear that the net result of all this pain going to be an increased tendency to extremism and an elevated chance of revolution: those are factors that are so random that who knows who'll come out on top?
Also, in reference to the UK, there's a stronger separation between people and companies than in the US; the tax system differentiates so that personal taxes aren't done using the same set of rules at all as companies are taxed under. This greatly reduces the amount of annoyance experienced by individual citizens, since all the rules aimed at complex business arrangements are only experienced by those who are actually running a business: people still grumble about how high taxes are (of course!) but not nearly so much about the complexity.