Well that’s assuming that purchasing your home is your only investment. Many people who own their homes also own stocks, mutual funds, 401(k)s and even other real estate from which they derive rental income from.
My rule of thumb is that no investment should comprise more than 5% of my net worth ... or 10% for a "closely held" investment (like an ownership stake in a self-managed company). I'd consider a home a "closely held" investment for the sake of this discussion, which means I would not be comfortable with $500,000 of equity in a home unless my net worth exceeded $5 million. In that kind of scenario I'd think that an "own vs. rent" discussion is largely academic.