An additional weakness of this password system is that it renders the system far more vulnerable to brute-force hash cracking by techniques such as rainbow tables. This could happen if your password hash database was leaked in some way.
If an attacker has gained access to the hashed password database, the two passwords would have to be stored separately as two hashes (since storing them together prevents direct comparison of each password). This therefore greatly reduces the entropy of each hash, allowing an attacker to easily crack both hashes far faster than it would take to crack one single hash of the concatenated passwords.
If the two passwords are of equal lengths and are drawn from the same pool, the time taken to crack two hashes in isolation takes half the exponential time (i.e. if cracking the full hash takes 1,000,000,000,000 tries, it would only take 1,000,000 tries to crack each sub-hash).
A good case study of this is the NTLM hash used in Windows XP and below, which has a design flaw very similar to the password system mentioned. A relatively strong password is split up and stored as two separate hashes, which makes the entire password significantly weaker.
Even computers of 10 years ago could easily crack the vast majority of NTLM hashes in a few days without using rainbow tables, and with the tables, the cracking is almost instantaneous.