your leaning forward is more of a sign of your intent to increase your 'life' (or , energy). For some horses , this is enough to trip them over into a canter. For others, they become irritated, and simplly run faster at a trot becuase they feel the sense of falling forward, or , at best, being 'tipped' forward.
If a person wishes to have a horse step into the canter from the hind end, rather than from 'falling' into the canter from the front end, they need to take a bit more time to ask the horse to set itself up correctly, to pause momentarily, and to strike off with the outside hind FIRST. This produces a canter depart that is uphill in nature, while riding a horse forward in a faster and faster trot, and leaning forward, will often 'tip ' the horse over from a trot into a canter, and it is initiatied with the front feet first, so starts with a downhill orientation.
Both canter departs have their place. But, asking a horse to gather itself, slow for a split second and depart into the canter from a hind end produces a more elevated and collected canter.
It really depends on what you are seeking. If you want to set the horse in a very specific lead, so that you can canter best an upcoming circle toward the left, for example, you want the horse to strike off with his outside RIGHT leg, and you will need to have a very fine control of that.
If you are simply ambling down the trail and you decide to have a faster gait, you can simply increase the 'life ' in your body (transmit the intention to go faster) by leaning forward and perhaps raising your hand, and perhaps kissing . . and your horse will pick whichever lead it naturally falls on . . . and you'll go forward faster and have a lot of fun.