My wife is a lawyer. She sometimes has to deal with people who think they know the law as well as she does (or better), simply because they've read the written laws or they've read the contract. That is almost always a huge mistake.
What is written is only one leg of the tripod. Another leg of the tripod is knowing the legal precedents, and you won't get those just by reading the laws or the contracts -- and even if you pass the bar exam, you probably won't learn those outside of going to law school. The third leg of the tripod is knowing which judge(s) you are dealing with, and how they are likely to rule, based on what is before them -- and even law school can't really help prepare you for this problem.
And all of that assumes everyone is operating in the same legal regime, in the same jurisdiction. The legal systems can be radically different in other places, such that the lawyers in that area don't even think the same way. For example, in French law, there is no Federal system. So, any contract that is written with language referring to federal law may be null and void in France -- just ask Chubb and their multimillion dollar case that went all the way up to the French Supreme Court.
So, as a programmer, sure -- you can read the contract, and you may even be able to do a better job of it than most. But do you know all the legal precedents in your jurisdiction? Do you know all the respective judges who might see your case and how they would rule?
If it's a standard contract with a big company, you may just have to bite the bullet -- or decide you don't want to work under those rules.
Either way, a big company probably isn't going to make any changes for you, because this is their standard contract that they give everyone, and they never make any changes for anyone.
So, how badly do you want this job? How much of a stink are you willing to raise to try to get changes made to the contract, before you decide it's not worth it?
Even if you are a lawyer, if you are a client in a case, you don't want to represent yourself. You can't really be properly impartial when it comes to what you want, and so you would be the moron who would be retaining a fool as his representation.