We have no reason to think Marcus Aurelius disliked Commodus. There are bits and pieces of private writings that tend to point to the idea that he was very fond of his children.

When Commodus was quite young Marcus’ tutor Fronto wrote:

I have seen your little chicks, and a more welcome sight I shall never in my life see, so like in features to you that nothing can be more like than the likeness.

Fronto II, Loeb, 119.

Commodus and his twin brother were very young at this time, but I doubt Fronto would have said such a thing if Marcus was not doting upon his children.

Later, Marcus himself writes:

…to show… your children unfeigned love (I.13)

…I had good grandparents, a good mother and father, a good sister, good teachers, good servants, relatives, friends – almost without exception…

That my children weren’t born stupid…

That my children had competent teachers… (I.17)

We also know Marcus was very worried about Commodus’ health. Marcus ordered the great physician Galen to keep an eye on Commodus.

He instructed Commodus’ educator or tropheus, Pitholaus, to send for Galen ‘to attend his son, should he ever fall ill.’ (Anthony Birley, Marcus Aurelus p. 162; Galen, On Prognosis, 9.6)

Marcus may have seemed cold towards Commodus, but we need to remember that Marcus was a practicing Stoic, and they earnestly believed they shouldn’t become too attached to things outside their control. Many children died young in that era, and this could be devastating to the parents. To combat this Stoics sometimes performed exercises like the following. They tried to teach themselves that death was not something evil.

Start praying like this… Not ‘some way to save my child’ – but a way to lose your fear. (Marcus IX.40)

Marcus often writes about losing children, so this was something which obviously bothered him.

Edit:

I just remembered this passage from Birley:

In a few places [in Meditations] one might detect references to Commodus, for example, ‘If you can, convert him by teaching; if not, remember that kindliness was given to you for this very thing;’ ‘if he makes a mistake, teach him with kindliness and point out what is being overlooked; if you fail, blame yourself, or not even yourself;’ ‘kindness is invincible… what can the most insolent do if you continue to be gentle with him and quietly show him a better way at the very moment when he tries to do you harm – “No, child, we were born for other things, I shall not be harmed, you are harming yourself, child”.’

Anthony Birley, Marcus Aurelius, p.218

However, as Birley himself points out that these passages do not necessarily refer to Commodus. There are no subjects listed, so any attempt to tie these to Marcus’ son is purely speculation. It is likely that some historians thought Marcus disliked Commodus (it is an ancient idea) and so tried to find passages to ‘prove’ it.