Put simply, the arguments against are that anything between the lens and the subject can only degrade the image. Adding a filter can also make a lens more susceptible to flare, particularly with the lower quality filters.
The arguments for are that if you have a minor accident, a scratch on a filter means you can junk the filter and fit a fresh one - for relatively low cost (compared to a new lens) you are back as if no damage had occurred.
Which option is right for you depends on you and what / where you shoot.
At one extreme, if you are careful, and shoot landscapes of gently rolling hills, or still life in the studio then there's no benefit to filters.
At the other, if you are accident prone, and shoot rally-cross (mud & stones everywhere!), or from racing yachts, then a filter will be a definite benefit.
Most are somewhere between these, and it's up to you to figure out if the benefits outweigh the disadvantages.