From a procedural standpoint, dives involving gas switches are normally made with the greater percentage of oxygen and lower percentage of nitrogen being used as the deco gas. For example, switching from gases like trimix, nitrox or air used in the deeper portion of the dive to gases such as 32% nitrox, 50% nitrox or 100% oxygen will aid in decompression by reducing the amount of inspired nitrogen allowing more nitrogen to be eliminated through respiration as a diver ascends. Switching to a higher percentage of oxygen and lower percentage of nitrogen will also change the gradient and the driving force from a decompression theory standpoint with the gradient being theoretically more favorable if switching to gases with lower nitrogen percentages as pressure on the tissues is reduced during ascent. This is usually a more advantageous and safer gas switch than switching to a higher nitrogen percentage. However, even for dives in which a gas switch is planned to accelerate the decompression, it is possible to lose the deco gas and find yourself decompressing on your back gas or on another gas source. The other gas source might be air. This would be a fairly common scenario for a recreational diver in an emergency. You can imagine a diver at 100 feet on nitrox running low on gas during a wreck dive in Florida and gaining the attention of another diver using air. Once the emergency is handled the nitrox diver ascends breathing air and should probably lengthen safety stop times as a precaution for avoiding DCS.
As for using air over nitrox to lengthen dive time, when running the possible strategies on V-Planner (nominal conservative settings), we can compare the following dives:
If we use 32% nitrox for 20 minutes at 100 feet then switch to air for 10 minutes to extend our bottom time and ascend on air, V-Planner asks us to do a 40 second mandatory decompression stop at 30 feet, another mandatory deco stop for 3 minutes at 20 feet and finally a mandatory deco stop for 7 minutes at 10 feet.
Reversing that to using air first for 10 minutes at 100 feet then 32% nitrox for 20 minutes at 100 feet and ascending on the nitrox 32%, V-Planner asks us for a mandatory 2 minute decompression stop at 10 feet.
Had you made that dive, you would have been better off using the pony bottle first. Not only that, but if you encountered a problem such as a bcd malfunction and you needed to lighten your load, you could shed the pony bottle and have the greatest amount of gas saved for the end of the dive on your back. Most divers tend to exhaust their primary gas supplies and then switch to a pony. But, one technique for deep diving is to carry a stage bottle and use that for the bottom portion of the dive leaving the gas on your back untouched and employing another bottle or other bottles for decompression.
You did the correct thing by not diving without adequate training and understanding. It's commendable to be able to say, "No thanks!" when faced with peer pressure. Sometimes our friends mean well, but if we mean anything to our friends we always hope they'll be supportive and understanding when we thumb a dive whether underwater or at the surface.
