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Although we can not be certain how Clark Howard came to that figure, my best guess is that it is based on the tax rates in effect in 2004, the year of the article.
According to 2004 Tax Rate Schedules: Marginal Ordinary Income Tax Rates for 2004 the highest marginal rate was for taxable income over $319,100.
Allowing for at least the standard deduction and exemption amount the total income would be close to the $350,000 amount in the article.
Presumably Mr. Clark was not saying that if your income was $349,000 that this type insurance is not to be considered; but was likely using that round number of $350,000 as the a reference to those in the highest marginal tax bracket.
My reading is that was not an exact cut-off; but rather an example of the range of income under which he opined that insurance should be considered.
There would be no reason to have an exact cut-off; but it would make sense to refer to an income amount rather than taxable income or highest marginal tax rate as the use of the $350,000 would mean more to most people than reference to taxable income or marginal tax rates.
The main disadvantage of variable universal life insurance is that the fees within those policies are usually much higher than if the same assets were held in mutual funds or another vehicle.
Also, the premium for the permanent insurance will be higher than a comparable term policy with the same face value. There may also not be a real need for the entire face for the lifetime of the insured so term would be better in that case.
Policies can lapse or require additional premiums if the investment performance is not adequate.
See the article, for example, at Variable Life Insurance, Universal Life Insurance, And Variable ... for more details (and note gross rate discussion).
Please understand that I am not currently licensed as an insurance agent and this is not insurance and not investment advice (even though I am a Registered Investment Advisor currently).