Thing of 私は as the topic here rather than the subject, and it will clear up your problem.
I you less than tall >>> “As for me, you are less tall” OR “In reference to me, you are less tall.”
You are not the SUBJECT of the above statement, but the TOPIC. The height comparison comes from your height as a baseline, but you yourself are not acting upon the (assumed here) copula.
If you added in the です, your interpretation would indeed result as "I (私は) am (です) less tall (より高い) than you (あなた). But take out the 私は and you’re left with "You (あなた) are (です) less tall (より高い).
「あなたより高い」alone simply would be “you less than tall,” which perfectly changes to “You are less tall.” The use of 私は is unnecessary here, as Syphus said, and I think it’s what’s messing you up. Does this approach make any sense?
Textbook Japanese teaches us to think of 私は。。。です as “I am…,” but that’s not accurate to how the grammar actually works.