I recently figured out the recipe for garlic vegan butter which is made primarily by roasting garlic, then whipping it in a blender with coconut and olive oil, and cooling in the refrigerator. It's delicious, textured similarly to butter and, as far as I know, not terribly unhealthy.
Then my father mentioned to me that that is similar to the process of making hydrogenated oils. I DO remember once reading something about whipping oil being a bad idea. Is that true? Am I basically just quaffing hydrogenated fats?
Oil is hydrogenated by bubbling hydrogen through it at high temperature (on the order of 400 to 500 degrees F), in the presence of a catalyst such as nickel.
Air is 0.00005% hydrogen, you are probably not using temperatures high enough, nor doing it for a significantly long period of time, nor having an appropriate catalyst present. The amount of hydrogenation introduced via this recipe is somewhere between none and vanishingly small.
However, coconut oil itself is about 92% saturated fat--which means the fats are naturally saturated with hydrogen. While a natural saturated fat, not a manufactured one, coconut oil is saturated.
If your recipe is delicious and you enjoy it, eat up in moderation like anything else (chocolate excepted). :-)
Manhandling oils in a blender can cause some of them to be oxidised (eg sensitive olive oil), giving off tastes.
Hydrogenation, as described above, is a completely different process - which IS used to create fats that behave like room temperature solid, saturated fats from room temperature liquid oils.
What this recipe is likely doing is emulsifying the oils to achieve a solid result (similar but not identical to a stiff mayonnaise)...
Your father is probably confusing the process of making margarine from saturated fats with the process of hydrogenating fats, which used to be the primary way we got saturated fats for making margarine. The two are completely separate though.
Margarine is made by emulsifying a mix of saturated and unsaturated fats with a small amount of water in what amounts to a specialized blender. Originally margarine was made from animal fat. Later artificial saturated fats were produced by hydrogenating vegetable oil. Now palm oil is used which doesn't require hydrogenation but which does have issues of its own. Clarified butter could probably even be used to make margarine although it would be kind of pointless.
So what you are doing is not that far off from how margarine has been made since the switch from hydrogenated vegetable oil to palm oil. You are just using a blend of coconut and olive oil in place of the palm oil and vegetable oil used in most commercial margarine and you are using garlic as the source of moisture instead of just water. Your general purpose blender also probably isn't as good at forming the emulsion as dedicated margarine blenders.
Ultimately, you are making margarine or something very similar, but it is not hydrogenated any more than modern commercial margarine is. It's really not that different from other forms of emulsion like mayonnaise, vinaigrette, or emulsified pasta sauces like carbonara, although some of those also include chemical emulsifiers like egg yolk or mustard to help hold the emulsion together. Margarine relies on the saturated fat to physically hold the emulsion instead.