Is it acceptable for a student to connect with a professor on LinkedIn?

It sounds to me that this is just the reaction of that particular professor, and so there's not much you can do about it. Perhaps the professor only likes to use LinkedIn to connect with other researchers and professors, but personally I don't believe that it's unprofessional or inappropriate for university students to connect with professors. You are both adults and the site is intended for networking in the professional context. I myself added many of my lecturers on LinkedIn while I was an undergraduate, with no problems.

If you'd added him on Facebook, that might have been a different matter, as many people want to keep their work and personal lives separate and would regard such a friend request as overstepping that boundary. However, all you can do now is move on. In the future, perhaps only add professors that you have got to know quite well, as then they will recognise you if you request to connect, which in turn will hopefully mean they are less likely to refuse.

Yea that's rubbish - most academics have huge networks on Linked In. Many of their contacts are former students who have remained active in their field. This is particularly the case among graduate students and academics in their department.

Personally I think if an undergrad made the effort to connect on Linked In I would take that as a sign that they were motivated and keen to continue working in whatever field it was that prompted the connection.

If an academic is chastising a student for trying to build their professional and academic network - frankly I would just call them an idiot.

Don't be deterred! Keep building your network but seek out the enlightened people who thrive on making connections. Avoid the morons that refuse them...

Here I quote the crux of your situation, and put in bold font your sentence containing a question:

"I sent a connect request to one of the professors I had last semester (along with some other profs, most of whom accepted) and he just wrote back to me saying it is extremely unprofessional to be trying to connect on LinkedIn for a student/prof relationship. I am confused - how is this unprofessional and how can this be handled better in the future?"

Here is my answer:

• Whether or not it is unprofessional is extremely subjective.
  
• What you did is perfectly okay, perfectly legal, and is done very frequently by many people.
  
• My recommendation: feel free to continue connecting with people as you see fit, but be aware that some professors might not like it. Exercise careful judgement: if the professor has 5 mutual connections with you, and 4 of them are students, go ahead and connect with them. If they have < 100 connections in total and in real-life you are able to see that they are not the type that would ever want to connect with a student, proceed with caution if you think you might want something from that professor later.