Trees can be too close to the house for several reasons. One is that if the tree overhangs the house, insects may move from the tree onto the roof, and eventually into the framing. This problem can be alleviated by trimming. Another problem is that a tree too close to the house can fall in a storm and damage the house. No amount of trimming is going to alleviate that problem. Another possible problem is that the roots of the tree can damage the foundation, or get into sewer or water lines. Trimming will not help that situation.
The federal list in my link lists 12 common species of birch tree. You did not indicate which type you have. Due to differing local terminology, calling a tree a "white birch" does not really help. Better to use the formal Latin name to describe your tree, if you know what kind of tree it is. See http://www.fs.fed.us/ne/morgantown/4...tr/table3.html
for help in proper naming of your tree.
Knowing what kind of tree you have is immensely helpful in deciding what to do with it, for example yellow birch Betula alleghaniensis
is a long lived tree that grows over 100 feet, and can get more than three feet in diameter, and you almost certainly don't want one of them near your house (treefall damage problem). Other species only grow 30 or 40 feet at most, and may not pose a treefall problem.