Your misunderstanding is that a subsidy is not aimed at one US farm versus another, it's US farms versus foreign farms.
The reason should be pretty obvious, without the subsidies they would be no US farms. And then in time of war there would be trouble.
There are a huge number of US industries that exist only to make sure that US capacity will remain even in time of war.
The same goal could be accomplished with tariffs, but then the price of food would be higher.
The claim implied that the small farms get more of the subsidy, i.e. that they would be the ones wiped out without it.
> The reason should be pretty obvious, without the subsidies they would be no US farms.
Why would there be no US farms? Real estate in San Francisco is much more expensive than it is in Mexico City or the like, but farmland in Oklahoma is not uncompetitive with farmland outside of the US.
If this was the real reason then the subsidies wouldn't be suspiciously concentrated at the location of Iowa caucuses.
Politicians are crafty buggers who will repurpose anything they can to provide themselves with an edge, so that doesn't necessarily say anything about the theory behind the subsidies.
I would definitely argue that there are simpler ways of helping low-income families to afford food though, if that is your goal... just lower their taxes further, or give them negative tax / UBI if they are already paying no taxes, rather than adding lots of complex gears to distort the economy to try and affect the same outcome. Or more food stamps if you don't like the idea of poor people spending their tax rebate dollars on non-food items that they prefer.
That's assuming that you would lower taxes uniformly instead of e.g. lowering them for the lowest tax bracket, which is in no way required.
The subsidy argument is a scam anyway. It's a commodity market. The margins will be razor thin, the end. If you subsidize production, prices go down. It will eat the whole subsidy and leave the margins razor thin.
The only way the subsidy helps you is if you get more of it than your competitors. Now who do you think that applies to, the family farm or the huge corporation with lots of lobbyists?