There are also times when they can't [give you extra time]...or when to give you that two weeks means taking it away from your collaborators; i.e., the artist is going to have to draw the comic in three weeks instead of the five he expected to have.
You may also have harmed his income. He expected to have that script next Tuesday. He planned his life and maybe turned down other work so he could start drawing your script then, plus he counted on being paid for it by the time his next mortgage payment is due. But because of you, he has nothing to draw next week and no way to make money on the days he cleared to draw your script...and he may have to turn down the assignment he was going to do after he finished your script because he's now not going to be done with it when he expected to be. Ask anyone who's worked in comics for a few years and they'll gladly unload a tirade of anecdotes about how someone else's lateness screwed up their lives and maybe even prevented them from doing their best work.
The above advice, as I said, is aimed at a writer for the comics market, but it is relevant to animation artists. Company-produced comics and company-produced animation are both pipelines. If you are an artist in working in either, there is somebody ahead of you and somebody following you in the pipeline. If somebody ahead of you is late, you've got less time to do your job; if you're late, somebody after you has less time. No matter what the length of the schedule, it's a standard complaint that you wish you had more time.
Two things flow from hitting deadlines: payment and return business. Companies don't get paid the full price of a job until it delivers and if it delivers late, a late payment can jeopardize a company's existence. A company that delivers late is likely to lose a client. A company that consistently delivers late is a doomed company.
No company will risk its existence on an employee who misses deadlines. Whether a project is a TV series, feature film or videogame, it's likely the budget is in the millions of dollars. No artist is more valuable than the company's existence or reputation, so artists who can't hit deadlines are artists who will spend more time unemployed.
Yes, the people setting up the schedules or passing judgment on work are often ignorant. They create impossible schedules or ask for changes that will take enormous amounts of time. It's the nature of the business and everyone has experienced it. It is better to avoid these projects and people rather than commit to them. Experience helps to read the situation, but things sometimes take a turn for the worse even if the project looked to be well organized at the start.
As Evanier says,
I tell beginning writers, "Never get a reputation for unreliability. You will never lose it," which is an exaggeration but only a slight one. What you need to do now is cultivate the opposite rep and maybe, just maybe, the new one will trump the old one. If not...well, you just may have to look for another career.