Otherwise the saddle risks to tip under the horse belly when you prepare to saddle up and then the horse gets scared and risks to bolt wherever he sees fit from such a clown. The classical method starts in 2 movements. Get on the left side of the horse, take the reins in your left hand, put your left foot in the stirrup and it is your right leg that will give you the push over impulsion to climb aboard. This attitude will take you a few hours to acquire. Thus you will be able to feel the horse, also to dose your effort and also to be able to keep a better handle.
Most beginners feel unstable and ask to rise up their stirrups.
In western horse riding the legs hang down naturally along the horse hardly placed on the stirrup. This instability impression is normal and will disappear only after several horse riding. Thus he will not dispose of you according to his own humour. Know that the horse learns quickly of the weakness of the rider. Just press down a bit using your 2 heels.