Full disclosure: I have not read the book that purportedly promulgates this myth, but was tipped to it by FoIB Wenchy. So I won't take the author to task, but merely use her premise as a "jumping off point" to discuss how the concept is so deeply flawed.
First, though, let's review how permanent life insurance works, and why it can be such a useful tool. Insurance is about risk, and life insurance is a particularly good example of why that's important. Life insurance is based on the premise that death is a certainty; the only question is when (and, in some cases, how, but that's another post). Notwithstanding the very useful LifeSpan widget we've previously discussed, no one but the guy on death row really knows when he's going to die (and he's not a particularly attractive prospect for most carriers). Since we don't know when, we buy permanent insurance as a tool to minimize the financial risk to our families.
To do this, permanent plans cost more than they need to in the early years, as a way to sock away reserves that keeps the plan affordable as we age. These "cash values" are comparable to the equity one builds in one's home, and can be used as a sort of savings account that can be accessed should the need arise. And just as one's house is the collateral for a home equity loan, the death benefit of the policy is the collateral for the policy loan.
Pretty simple, really.
Life insurance policies are rarely good "investments," however, and should never be confused with such. While the cash value builds on a tax-deferred basis, and can be accessed on a tax-advantaged one, they're really not cost effective as ATM's. For one thing, interest is charged on these loans; left unpaid, this can snowball, and even cause the policy to collapse.
For another, if one dies with a substantial loan against the policy, funds that had been counted on to help the family are unavailable at a time that they may be most needed.
But perhaps the benefits of the plan outweigh the drawbacks:
First, the most essential thing to determine when buying a policy - any policy - is how much one needs. Simply buying a policy for use as a potential cash cow is dangerous, and I would also characterize an agent who sells this way as ethically-challenged.
Second, it presupposes that one can find (and afford) a "participating" policy (one which pays dividends). These are not bad policies per se, but they can be more expensive than non-par plans, particularly Universal Life policies (which have their own issues, as well). And, of course, that one can afford to maintain the premiums on such a plan; as we'll see in a moment, letting the policy lapse (or "be foreclosed" to continue our homeownership analogy) can have serious tax consequences.
Third, dividends are not guaranteed; relying on them can lead to disastrous results. If they're lowered, or suspended in a given year (or years), the whole concept collapses. Skeptical? Ask a (former) Crown Life insured.
Fourth, by definition one cannot "reinvest" in a participating whole life policy, because there is no "investment" to be made. Lest readers think I'm parsing, be aware that policies which have investment-like components (called "Variable Life") are heavily regulated by federal and not just state agencies. They require special licenses and documentation, and more closely follow "the market" than the participating whole life plans suggested by the reviewer.
Fifth, interest on life insurance loans is not tax deductible, and hasn't been for many years. So any potential tax savings touted are nonexistent.
Lastly, let's talk about this "paying yourself back over time" nonsense. You're not paying yourself back: you're re-paying the insurer, which holds the death benefit as collateral. If one were to falter in that planned repayment, the possibility that the policy will lapse increases. If one doesn't need the plan anymore, then the loss of the potential death benefit is not a problem. But if one has borrowed out more than one has paid in (a very real possibility with a plan that's been in force for a while), and subsequently lapses the policy, the gain is fully taxable.
Kind of shoots the ol' ATM in the foot, doesn't it?
The bottom line is: this is a very bad idea. As I mentioned above, there are some really great reasons to own permanent insurance (I own three such plans, of varying design), but the idea that one can effectively use any one of them in this manner is at best silly, and at worst dangerous. Unfortunately, by the time one learns this the hard way, it may well be too late.