I think the literal translation might sound a touch unidiomatic, but not terribly strange.

He could not want anything against him.

But in English, I would say the idiomatic expression that most closely approximates this usage is hold instead of want.

He could not hold anything against him.

First, en vouloir has not only the meaning to blame someone :

• Avoir contre quelqu’un un sentiment de malveillance. (To have against someone the will to harm)
• Attaquer, tenter de nuire à quelqu’un. (To want to attack or to be detrimental to)
• Avoir une rancune vis-à-vis de quelqu’un. (To have hard feelings or grudge)
• Avoir quelque prétention sur une personne, sur une chose, en avoir quelque désir. (To desire)
• Avoir du regret, du repentir. (To regret)

And it can also means

Être très déterminé, très motivé. (To be motivated, determinated)

To help you to understand, you have to place yourself in situation:
Something happened, probably caused by someone and you :

• want revenge / to ask for compensation (3 firsts meanings);
• want to have / get it back (to desire);
• want to have done differently (to regret).

→ You want to have something from this person. (excuses, goods, feelings)

→ You are refusing the current situation and want reality to change.

You can look at the reverse translation to have more traductions.

I believe it came from « vouloir du mal à quelqu’un » which is shortened to « en vouloir à quelqu’un » long ago