Triathlon run training has two primary challenges. First, running is a more structurally demanding sport than cycling or swimming. Meaning, the fatigue and injury risk is greater. Many triathletes don't come from a running background which exacerbates this. In the end running demands respect and you have to be careful about overdoing it. Being able to supplement cycling and swimming helps prevent run overtraining.
Second, many triathletes view cycling as fun and social, while running is hard work that must be done. While two people of differing abilities can easily ride together and still get in a good training session, running will more widely divide abilities and can become a more solitary sport.
That's not to say that running can't be fun and social, but it takes a bit longer to develop "easy running" fitness and often a paradigm shift in approach to training. I often see athletes who are convinced they're too slow to run with other people. This is rarely true.
Finally, triathlon is a single sport made up of three pieces. None of those pieces stands alone when it comes to training. Rather, strength in any given sport can benefit the other two. If you focus on bike training you may be fresher coming into the run and thus run better. Focusing on your run will improve your run fitness and often improve your power and efficiency on the bike as well. The trick is to look at each sub-sport as a part of the whole.
More: 10 Steps to Designing a Training Plan
Usually the answer to "which sport should I focus on most" is, focus on the sport of triathlon. Design a training plan that not only helps you develop as an athlete but is fun and interesting. Often this will be a plan which alternates "focus weeks". One week may be more cycling, the next more running, the week after that may have more swim focus.
I often have my athletes pick small goals or single sport races to aim for during a focus week or block of training. Triathlon is still the primary goal but doing single sport races can build single sport confidence that will complement triathlon performance.
Most importantly find a balance that works for you and keeps you motivated and excited about your training.
More: 5 Keys to Long-Course Triathlon Training
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