ETA: The fastest way to financial independence is not increasing income, it's reducing expenses. You can easily retire right this moment if you reduce your expenses.
Technically, this is not always true: no amount of expense reduction (even to $0) would allow you to retire on a negative net worth.
However, under more reasonable assumptions, I agree.
Under "more reasonable assumptions", increasing income will lead to retirement faster than decreasing expenses, because under "more reasonable assumptions" (including an assumption that a person will be spending more than zero dollars in retirement), decreasing expenses may already be impossible.
An example set of "more reasonable assumptions" might be a person just starting at age 18 with a net worth of zero and a salary of $20,000 per year (net of tax), and who currently spends and plans to retire spending $10,000 per year. If the person refrains from increasing income, and assuming they keep their money in cash and plan to retire when they hit $250,000 (25 times their expenses), they can retire after
25 years of work. By contrast, if they simply increase their income to $260,000 (net of tax), then they can retire in
1 year of work. This is nothing new though; I've explained this in countless posts and we are all well aware of it.
In order for decreasing expenses to lead to a faster retirement time, there has to be
room for decrease. As I've pointed out myself, it's possible to get expenses pretty low and
retire on a relatively small sum, but if you plan to do anything at all in your retirement, you are likely going to need
some money, and, therefore, increasing income is going to enable you to reach retirement faster, whereas decreasing expenses
can't help if you are already spending the minimum (which is a reasonable assumption for a Mustachian).
Dude, ...
Did you just assume my gender?!
Your other points are without merit, but here you raise a fair complaint.
As you know, I didn't actually make an assumption about your gender; rather, I was using "dude" in a gender-neutral sense to mean something to the effect of "you can't be serious", but, as you point out, that was actually problematic of me, because notwithstanding common usage, the term "dude" clearly has a masculine origin. It is at least arguably kyriarchal to subsume the feminine into the masculine in the English language. As Jack points out, this tradition has a long history, but sexism also has a long history so that isn't much of a defence. I retract my use of "dude".