Great question. Just as most humans have a dominant hand, many horses are sided and have one hindquarter that is weaker than the other. And, of course, if the issue is simply that the horse is weaker on one side, this can be improved with conditioning and targeted physical therapy exercises. However, when there is notable asymmetry or differences in how a horse travels one direction compared to the other, often more is at play, and you and your veterinarian should consider lameness.
Think about the canter: It’s a three-beat gait with the outside hindlimb (beat 1), inside hindlimb and outside forelimb (beat 2), and inside forelimb (beat 3) moving in that order. Thus, the outside hindlimb is responsible for propelling the horse forward in canter (i.e., during the right lead canter, the left hindlimb is the driving limb). This is important to note because, more often than not, if a horse struggles in canter one direction, the cause is often an issue with the outside hindlimb. Additionally, horses with hindlimb lameness tend to move away from the lame leg. In the scenario you describe, the horse struggles more in right lead canter and tends to move away from the left hind limb, both of which might indicate an issue with the left hind limb.
This brings us to the heart of your question, which is how to differentiate between weakness and lameness. The first step is to have your veterinarian perform a thorough musculoskeletal and lameness examination on your horse. In many cases your veterinarian might be able to detect a lameness that’s not obvious to the untrained eye.
If your veterinarian doesn’t detect a lameness, he or she might recommend an anti-inflammatory medication trial, in which your vet prescribes a non-steroidal medication for five to 10 day while your horse continues in his normal exercise routine. If the crab-canter noticeably improves while the horse is on anti-inflammatories, that indicates the underlying problem is pain- or lameness-related. If the veterinary examination does not reveal any lameness, and the horse doesn’t improve on anti-inflammatory medications, then you might back yourself into the conclusion that you’re dealing with a training and conditioning issue.
The bottom line is that while either lameness or weakness could be causing the crab-canter,” lameness is a little more likely. So, I’d recommend ruling out lameness and/or musculoskeletal pain before concluding it’s a training problem. This serves two purposes: One is that it gives the horse the benefit of the doubt that there is a physical cause of the issue, and second, if is the horse has a lameness issue, knowing that allows you to address it sooner rather than later.