Why did Naomi raised Obed and not his mother Ruth?

It depends on how the question is read.

Why did Naomi raise Obed instead of raising Ruth?

Ruth was not Naomi's daughter, but her daughter-in-law, so it would make no sense for Naomi to raise Ruth. The two would have met, presumably, when Ruth was already an adult.

Why did Naomi raise Obed instead of Ruth raising Obed?

Presumably, Naomi wanted to dote on her step-grandson while Ruth continued to work in the fields. Additionally, Obed was now Naomi's male heir which made him very special to her in Biblical times.

Of course, it may well have been a Biblical mistake as well.