I would argue that any mounting technique that allows you to get starting riding the bike is correct.

I use primarily the technique you describe as I feel I'ts agile, stable and quick.

The argument of side load is bogus. If a bike broke during that maneuver It is unsuitable for riding. Also, it is the same as applying all of your weight on just one pedal. The angle would be the angle needed to keep the tire contact points in line with your body and bike's combined center of mass. In order to increase the angle, you'd need to perform a pretty weird mounting (or you are performing acrobatics rather than just riding).

However, there are a few situations where the cowboy mounting is less advisable or not suitable.

When riding a bike that has a loaded rear rack, the swing required may be too much to be comfortable, and depending on what you're carrying, the prospect of hitting your leg against it can be enough of a deterrent. (From experience I know it hurts a lot more on the downswing). Sometimes I've found myself carrying tall loads that would impede completely the cowboy mounting.

The other situation is when you are in a crowded space, like in a group ride or in a crowded street during a commute. It is very easy to loose track of whether you would hit somebody. You may check before, but for when you execute the movement, someone may have entered your movement path. You could also swing your leg too close for someone else's comfort. Finally, some loose matter from your shoe may fly into someones face, etc.

In those situations, for safety and for the sake of avoiding awkward situations, I mount by lifting one leg over the top tube.

Also, for starting on inclined, loose or irregular terrain, It's easier and sometimes the only way. When I need to start on a very steep uphill, on a mountain trail with loose rocks and roots I do leg over top tube, clip that foot (usually the right one) and lift the pedal near the top. At this point, I don't push on the ground with remaining foot in order to advance, I use the pedal instead. As soon as I start pushing on the pedal, lift the other foot and place it on the pedal. If done quick enough, I catch the pedal before the upstroke ends and is ready for the down stroke.

In conclusion, having more than one mounting technique is advisable and helpful, but ultimately anything that accomplishes the objective and does not hurt yourself nor others and does not damage your bike is correct.

I would argue that any mounting technique that allows you to start riding the bike is correct.

I use primarily the technique you describe as I feel I'ts agile, stable and quick.

The argument of side load is bogus. If a bike broke during that maneuver It is unsuitable for riding. Also, it is the same as applying all of your weight on just one pedal. The angle would be the angle needed to keep the tire contact points in line with your body and bike's combined center of mass. In order to increase the angle, you'd need to perform a pretty weird mounting (or you are performing acrobatics rather than just riding).

However, there are a few situations where the cowboy mounting is less advisable or not suitable.

When riding a bike that has a loaded rear rack, the swing required may be too much to be comfortable, and depending on what you're carrying, the prospect of hitting your leg against it can be enough of a deterrent. (From experience I know it hurts a lot more on the downswing). Sometimes I've found myself carrying tall loads that would impede completely the cowboy mounting.

The other situation is when you are in a crowded space, like in a group ride or in a crowded street during a commute. It is very easy to loose track of whether you would hit somebody. You may check before, but for when you execute the movement, someone may have entered your movement path. You could also swing your leg too close for someone else's comfort. Finally, some loose matter from your shoe may fly into someones face, etc.

In those situations, for safety and for the sake of avoiding awkward situations, I mount by lifting one leg over the top tube.

Also, for starting on inclined, loose or irregular terrain, It's easier and sometimes the only way. When I need to start on a very steep uphill, on a mountain trail with loose rocks and roots I do leg over top tube, clip that foot (usually the right one) and lift the pedal near the top. At this point, I don't push on the ground with remaining foot in order to advance, I use the pedal instead. As soon as I start pushing on the pedal, lift the other foot and place it on the pedal. If done quick enough, I catch the pedal before the upstroke ends and is ready for the down stroke.

In conclusion, having more than one mounting technique is advisable and helpful, but ultimately anything that accomplishes the objective and does not hurt yourself nor others and does not damage your bike is correct.