There are a few reasons to avoid knocking down historic buildings. I'd say even more important than character and history are things like land use. Many historic buildings were erected before shitty zoning policies and before ridiculous corporate-handouts like mandatory minimum parking requirements. Knocking down buildings in many cities means you'll never recover the density of the old buildings due to new set backs, etc. In those cases, it is unwise. Replacing an old row of pedestrian-friendly store fronts with one drive-through restaurant and tons of asphalt around it ruins a neighborhood.

But if the city of allows high density building, it's often a better choice to knock down and rebuild. If the city allows mixed use buildings, even better. Take the new dorm at NJIT "the View", as an example. It replaced a gorgeous, historic castle-like old school... sad, but the old school had been abandoned for the last 12 years because the maintenance costs were prohibitively expensive and the rooms were too small anyway. It was full of fire hazards. The new dorm uses the entire lot, has parking under. It's an example of great land use. My only complaint is that I thought they'd include a few store fronts that were accessible to the public at the street level. That would have been killer. But, overall the new building is a big improvement over an impractical yet charming old castle.