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Should extra credit be offered?
As a student myself, I both like and dislike the idea of extra credit.
At some point, it will help my grade when I need. But another time, difficult extra credit assignment discourage me performs in class.
For example, as finals are closing in, lot of students like me build up the anxiety right before the exam, trying to study as much as possible to get a good grade. If the professor offers extra credit and I did do it. I can still get good grade despite poor performance on the exam, therefore less pressure into the week of final. I do believe the end goal of education is gaining the knowledge, not punish for what you don't know.
On the other hand of the spectrum, extra credit are not always fair as professor claim to be. Not every student can attend a guest lecture on a Friday night, there always be a conflict. And what make me furious are those extra credits that have no relation to the course material. The cases maybe few, but the whole idea of second chance also can discourage one from try harder. Be honest, I hardly do my last homework if I guarantee an 90 from previous grade + extra credit bonus.
Thinking ahead, does the real world have extra credit? a second chance if you mess up?
I think the question really come down to what kind of education experience we are dealing right now and what should be for next generation.