When people need to live off there investments they often say to go for funds that pay high dividends, but I'm having trouble understanding what the difference between getting dividends, and selling a portion of a stock is.
The benefit is not in taxes.
When you sell a portion of your stock, you no longer have a portion of your stock. When you get a dividend, you still have a portion of your stock.
Dividends are distributed from the net profits of a company and as such usually don't affect its growth/earning potential much (although there may be cases when they do). So while the price takes a temporary dip due to the distribution, you're likely to get the same dividends again next year, if the company continues being similarly profitable.
If you sell a portion of your stock, at some point you'll end up with no more stocks to sell.
The OP should be commended for thinking deeply about this.
When a dividend is issued, there is a small dip in the price of the issuing company's stock. At this point, the investor owns the same "piece" of a slightly less valuable "pie" plus a dividend.
In contrast, if the investor owned a stock that didn't issue a dividend and sold a little stock each quarter to simulate the income that would be provided by a dividend, the investor would own a slightly smaller piece of the same sized pie plus some cash. As littleadv pointed out, eventually the investor will own no stock if she keeps doing this...except that's not strictly true (if we allow fractional shares) and it doesn't get to the core of OP's curiosity.
Let's go back to the dividend-issuing company's stock price. What if it didn't rebound in the days and weeks following the dividend payout? What if the stock price kept falling with every dividend? In theory the investor's pie (fixed number of shares) could become worthless. We know, of course, that the company would stop issuing dividends well before that point (take for example, GE's recent 50% cut in dividends).
Conversely, what if the hypothetical non-dividend-issuing small cap stock kept increasing in price? The investor would need to sell a smaller and smaller number of shares each time to get the SAME amount of cash each quarter (simulating a dividend). So the investor would have a smaller and smaller piece of a continually growing pie, but the investor wouldn't necessarily care. As long as the stock price keeps going up fast enough, the investor may never run out of stock because they are selling less and less every quarter. The only issue that arises is when it becomes necessary to sell a fraction of a share, but even this can be accomplished. And of course, symmetrical to the argument above, this company could start issuing dividends if it attains persistent and substantial positive cashflows.
Bottom line is that there is not a lot of material difference between (1) taking a dividend from a dividend-paying stock (and not reinvesting it) and (2) selling a small amount of a non-dividend-issuing stock each quarter to simulate a dividend. Practically speaking, you are likely to incur a commission in the sale of stock that you would not incur with a dividend. Commission aside, there is absolutely no guarantee that either situation is indefinitely sustainable, and for a single stock, both will usually fail on the timescale of decades. However, dividend-paying companies usually have persistent and substantial positive cashflow, which can be a driver of stock price and an indicator of longevity and competitiveness in the marketplace. In a bear market, it would also be more ideal to collect a dividend--especially if the company doesn't decrease it--rather than selling stock. However, in a bull market, that hypothetical non-dividend-paying small-cap stock may beat the snot out of the hypopthetical large-cap dividend-paying stock, and the investor could capitalize on this by selling more of the small-cap stock than usual each quarter in a bull market (to simulate the dividend) and put the excess in an interest-bearing account or bond and draw upon this instead of selling stock in a bear market.
You can seek returns through dividends ("income investing") or capital appreciation ("value investing") or some combination of both! At the end of the day, you hopefully have a positive ROI, and how you want to realize that profit (dividends or selling stock) is up to you. Just be aware that commissions eat into your profit.
In the US, dividends are presently taxed at the same rates as capital gains, however selling stock could lead to less tax owed for the same amount of cash raised, because you are getting a return of basis or can elect to engage in a "loss harvesting" strategy. So to reply to the title question specifically, there are more tax "benefits" to selling stock to raise income versus receiving dividends. You have precise control of the realization of gains.
However, the reason dividends (or dividend funds) are used for retirement income is for matching cash flow to expenses and preventing a liquidity crunch. One feature of retirement is that you're not working to earn a salary, yet you still have daily living expenses.
Dividends are stable and more predictable than capital gains, and generate cash generally quarterly. While companies can reduce or suspend their dividend, you can generally budget for your portfolio to put a reliable amount of cash in your pocket on schedule. If you rely on selling shares quarterly for retirement living expenses, what would you have done (or how much of the total position would you have needed to sell) in order to eat during a decline in the market such as in 2007-2008?