What makes the roots of a tree at times, interfere with the water that comes into your house?

They can also grow through the pipes if the pipes are corroded.

Clay pipes were the norm in older houses so the roots of trees could easily grow through them or around them and crush the pipes. The way to prevent it is to put the newer hard plastic pipes leading out of your house to the main water and sewer lines.

Only thing you can do is either plant trees with deep roots that don’t grow sideways or plant trees far from the house and pipes or don’t plant any trees.
If you have trees that are not to big you can trim them low so they won’t spread so much. Trees are like iceburgs. What you see on top is often smaller than what is in the bottom. So a really wide tree will grow lots of feeder roots that will spread out to feed. You would want those far away from your home and side walks. They will push into your basements, ruin foundations and sidewalks and driveways. Your longer trees will grow deeper roots.
But really there isn’t much you can do except cut it down and plant one that is not so invasive. A smaller tree.

I had a house where roots grew into the sewer line, clogging it. We had a service come in every year or two with a grinding tool on a snake to ream out the pipes.

It was freaky to watch the first time, it looked like the guy was pulling tumble weeds out of the pipes.

The roots can sneak in through the joints in the pipe, as pictured here.

As @jaytkay said, I’ve never had issues with incoming water and tree roots, only sewage lines. Trees love sewage lines.

@jaytkay Drat. I wish the plumber had told us that. It probably started with a small lead in the joint of a cast-iron drain line leading from the washing machine in our garage in our home back in Virginia Beach. Roots grew right through the joint clogging the line. A plumber ran a small video camera down the drain line to discover the problem, smack in the middle of our concrete driveway about half way from the house to the street. But the sucker never mentioned using a grinding tool. He wanted something like 10 grand to jackhammer our driveway and replace the whole line. We were about to move to Massachusetts anyway, so we just sold the house with an as-is clause.

Thanks all. So, this is maily old house problem I guess the newer houses are built with root problem proof?

Here is something.