There's a lot of opinions on this topic - duh, just like everything else pilots opine upon! - but "old wives tales" is not the way to make up your mind. Start with the engine manufacturer's recommendations for hours between oil & filter change, then consider how the engine is used (how often it cruises, any special ops considerations, such as training aircraft that do lots of touch'n goes, dust, cold vs. hot conditions, etc.).
I believe most of the manufacturers (generally, all two of them ... Lycoming & Continental) generally recommend to change oil & filter every 50 hours, or every three months, whichever occurs first.
Do you benefit from changing the oil more often? I dunno ... actual data would be nice to base that decision upon. Yes, the cost of oil & filter is less than the cost of an engine rebuild, but over the course of an engine lifetime, it's certainly not insignificant. If one is changing the oil much more often than needed, the additional cost, at roughly $90-100 per oil & filter change (for an O-360 that takes 8 quarts per change, and assuming you do it yourself and your labor is "free"), can add up to a considerable waste. If the engine needs a change every 50 hours and you do it every 25 hours instead, over the course of a 2,000-hr TBO, the extra cost spent on 40 unnecessary oil changes is 40 x $100 = $4,000 ... which is about 25% of the cost of an overhaul on an O-360. It's not insignificant, despite what some have said on this topic. It'll be double the cost or more if you pay your local A&P to do it for you.
Yes, as one poster said, engine oil does break down with use, but keep in mind that the typical auto engine goes about 180-200 hours between oil changes per manufacturer's recommendations. So at 50 hours, per aircraft engine manufacturer recommendations, this is a small fraction of that oil lifetime. Yes, aircraft engines are built to much looser tolerances because they're aircooled and not liquid cooled, and the blow-by is much more than a typical modern auto engine deals with., so the oil gets dirty faster ... but still, the effect on the breakdown of long-chain hyrdrocarbons from engine heat and the shear forces on the oil are still roughly comparable to what any four-stroke internal combustion gasoline engine experiences - right?
Bottom line - it seems smart go with whatever the manufacturer recommendations are, as modified by the actual use your engine gets.