Ok, so spoiler tags, because I’ll comment a lot of things from quite a few books.
[spoiler]There’s an old law that witchers will invoke as a reward called “the Law of Surprise”. Check this wiki link: http://witcher.wikia.com/wiki/Law_of_Surprise . Geralt invoked that law twice, and in both cases the result/reward was Ciri. Her biological father wanted her for political reasons - basically to give his empire an official “hold” on the land of Cintra, in the north. But the way he looked for her was risky to say the least, and threatened her life and the lifes of others.
In Witcher 3, Geralt has a lot of reasons to not like Emhyr. Emhyr doesn’t really love Ciri, he’s the Emperor of Nilfgard (which caused many problems for everyone, including Geralt), and he was behind the assassination of King Foltest, a crime of which Geralt was wrongly accused in Witcher 2. You can imagine that Geralt wouldn’t want Ciri, who he loves as a daughter (and to whom he’s tied in an even deeper way than that) around such a man.
And yet… he is her biological father, and Geralt knows Ciri has every right to speak to her biological father if she thinks she should.[/spoiler]