To understand why this is so, we must first understand what validity and reliability are.
Validity has to do with whether an assessment really measures what it is supposed to measure. For example, the SAT is supposed to measure how well students will do in college. If students who score higher on the SAT generally do better in college, the SAT will be valid.
Reliability has to do with whether the test yields the same sorts of results in multiple conditions. In other words, the SAT is reliable if someone takes it 3 times in a short period (too short a period to really learn much more) and gets a similar score each time.
A test that is valid is always reliable. That is because a test that truly measures what it is supposed to measure will necessarily measure it the same way every time. If you are really measuring how ready a student is for college (validity), your test will have to yield the same result for the same student each time (reliability).