Why is it important for an art conservation scientists to study the properties of a painting before it is repaired

Its not only important to study the properties of the painting, but also the surroundings and context of the damage. Many times, studying the entire scene carefully can lend clues as to how the damage was done, and it makes the process easier to reverse.

Art conservation is a very delicate process that takes time and patients. In essence, our job is to rewind time, without the use of a time machine. Knowing how the damage was done allows you to more easily work backwards to restore a piece. Also, its important to inspect the overall integrity of the piece before it is conserved. In some cases, selective conservation can be even more damaging to a piece.

In essence, and to answer the question most directly, it is important to fully inspect the piece before it is conserved so that it can be properly reconstructed in the most appropriate and least obtrusive fashion (generally, this is just basic repairs, and NOT following the same methods as the artist - using the same methods leads to ambiguity regard whom painted what, etc.). Repairs should always be done as discretely as possible, but all the while making it evident that the piece was repaired. This adds to its authenticity, etc. It should be noted that many conservation methods are highly controversial, and each shop/museum has their 'own way'.

If you're looking for a more in depth look at how this process works, The National Gallery of Ireland recently published the process they used to restore a century-old Monet. While I don't necessarily agree with all of their choices (as I said, controversial), this does highlight the process quite well.