From what you've detailed about your dad's medical condition, it sounds like he may have a myeloproliferative disorder - which is slow growing, and often people live for many years with it. It is only in recent years that it has been reclassified by some medical specialists, as a cancer.
You're right about the 'cancer' label. It somehow makes your dad's illness sound more scary - and the fact that he is needing chemotherapy may have made everything feel real. I think he might be feeling a bit scared too, and often when we're scared, it comes out as anger. He's also likely to be feeling tired and therefore not very patient with those he cares about.
As you recognise yourself, boys and their dads often argue...it's part of growing up, and as a teenager, you're finding your own personality, and discovering that you and your dad may have differing viewpoints on things. There may be times when you both feel cross with each other...but it doesn't stop the underlying affection you both may have. Your dad will know that - and perhaps understand how you feel. Finding the words to say what you feel deep inside, can be hard.
You have expressed your thoughts, hopes and fears very well here. Perhaps writing your dad a card or a letter, saying some of what you've said here, might help..? After arguments, it's natural to feel upset...your dad may be feeling the same. You could ask him some questions about how he's feeling, and how you can help him get through the treatment - he might be glad to know you're there for him.
The unknown somehow tends to feel more scary than the known. Ask your dad if he can tell you a bit more about his illness, and what the chemotherapy will be, and for how long. Accept that some days you will still argue...but after cooling down, and saying sorry, hopefully you'll both be back on track...
If you'd like any more information, or to talk anything through, please do get in touch with us.