“do not lean upon your own understanding.” The allusion here is to the walking staff that almost every man carried for support and protection (which is why Jesus allowed his apostles to take one when they traveled; cp. Mark 6:8 and commentary on Matthew 10:10). Men leaned upon their staffs in all kinds of situations, but they were notoriously unreliable for a number of reasons. If modern hiking is any guide to us, the most common reason a staff is unreliable is that it can unexpectedly slip, causing a dangerous fall. Also, a staff may break and pierce the hand of the one leaning on it. This happened often enough that the emissary of the king of Assyria spoke about it to the people in Jerusalem (2 Kings 18:21; Isa. 36:6).
Human understanding is like a walking staff. It is just reliable enough that people can begin to trust in themselves rather than in what the Bible says, but then unexpectedly it slips or breaks and causes injury and harm—sometimes great harm. Wise Christians always trust God and never completely trust themselves, allowing for the fact they may be wrong.