Some people prefer to train by themselves, some prefer a training partner, some prefer to work in a big group class. Everyone's different, and everyone has their own way of finding motivation to train. I always find training partners to be the best and worst way to motivate yourself to train. Sometimes you can build each other up and support each other, other times you can get in the way of progressing towards your goals. I'll explain the biggest pitfalls that can come with training with a partner, and how I find is the best way to resolve these issues.
The first issue that you may have is that the pair of you are on complete different levels in terms of experience and ability. This can be a blessing as well as a curse. The less experienced half of the pair may benefit from this pool of knowledge and skill, where as the other half may feel held back and that they can't push themself as much. Typically, the more experienced person may lose out in this situation. The easiest way that I think you can overcome this is to not train with each other every session. Ideally, what you would do is do a session together, teach the less experienced person a thing or two with their training, and then allow them to go and train independently so they can build on these skills at their own pace. The reason that I believe this works is because you can both get the benefit from training with each other, like motivating each other and enjoying the social side of training with someone, but when you train by yourself for a couple of sessions you can both still progress at your own pace. Therefore, no one is missing out on smashing their goals, all while you can enjoy each others company!
The second pitfall is the two of you having different goals. I typically see this between couples who want to spend some of their quality time in their relationship in the gym. Although the gym may sound like a good time to spend with each other and work towards your goals, you may find that you get in the way of each others goals. Typically this is because it's hard to programme a workout where you both work towards different goals. You may want to do different exercises, amount of sets, reps and intensity levels. All of this may need to change to support you individually. The way to get around this is to both train at the same time, but work on your own workouts, and then help each other where they need it. Although it may feel like you're not working together, this way of training gives you both the freedom to work towards your own goals but by training near each other you can still get involved in each others workouts.
A final pitfall is not motivating each other enough during the workout. Now I don't mean you both sit there and take the piss out of each other, I mean that you both send way too much time talking about how your day went, what your plans are for the weekend and your life goals. Don't get me wrong, training with someone does come with a sense of friendship and having a good chat, but it can be very easy to let the workout take a back seat and end up just having a catch up. You can easily have a catch up over a meal or a drink. When you're in the gym you might as well try and improve yourselves while having a laugh! The key to avoiding this pitfall is to be strict with how much time you are resting for, be cautious that you aren't distracting each other while you are working out, and remember you are allowed to see each other outside of the gym where you can have a proper catch up!
So there's free common pitfalls I see regularly with people who train with a partner. Remember, it is great fun to have a training partner, but make sure you are helping each other reach your goals!