Disclaimer; I don't own Agents of SHIELD
It hurt. It was irrational, it was petty, but it hurt. And for the life of him Coulson couldn't find a way to make it stop. No amount logic or fair minded reasoning was breaking through the haze of emotional thinking that had overtaken most of his thought processes. He had said it himself, she wasn't his daughter, he wasn't her father. Cal was. And memory or no, he always would be. He would always have a piece of Skye's heart that Coulson could never truly have.
She wasn't obvious about it. For all the attention she could demand, Skye excelled at subtlety when she wanted to. She might have even gotten away with it too, but she fell asleep at the wrong time in the wrong place (the middle of the day in the team room) and Coulson just happened to walk by and saw her opened laptop. Honestly, he didn't really blame her for hacking into the security system of her father's veterinary clinic. After all, there was a time in his life where he would have done anything to just see his father one more time. No, he didn't blame her at all.
He knew that she hadn't gone back to see him after the first time. He knew she wanted to. He wasn't blind, nor was he stupid. He figured the only thing that kept her from going was the knowledge of how unstable the T.A.H.I.T.I. program could be, and the consequences of Calvin Zabo ever retaining his memory. He was better off now, Coulson really believed it, and to a point he knew Skye believed it too. Still, for a young woman to have to face the reality that her father was better off without her in his life, it was crushing and it was cruel. Skye had too much of that in her relatively short life.
In the span of a few short months, she had found her parents and lost them. Now, all she had left of either of them was nightmares of her mother trying to kill her, and sometimes adequate black and white security footage of her father who could never know who she truly was. Maybe it would be better if he discouraged her watching her father. It probably would be, but Coulson couldn't convince himself that it would be coming from anywhere that wasn't personal. As long as it didn't interfere with her work, there was nothing wrong (sans some illegal hacking, which they did on a daily basis anyway) with what she was doing. It wasn't necessarily healthy, but it was far from unhealthy.
Coulson was acutely aware as to why it bothered him so much. When he had joined S.H.I.E.L.D he gave up on the life that included white picket fences and PTA meetings. He thought he had made his peace with that a long time ago. Then there was Skye. She came crashing into his life and changed everything, changed him. And for the first time in years he wondered what his life could've been like had he made a different choice. Somewhere down the line, she became more than a consultant. Skye was his in everything but blood, and even then, the T.A.H.I.T.I. project blurred even that distinction. Having someone else in her life that was her father in both blood and love, it hurt. It wasn't jealousy per se but there was a certain sadness.
Coulson didn't hate Cal. He didn't agree with most of his choices, but all of Cal's actions were to help Skye and after all, most would agree that Coulson himself wasn't too clear headed when it came to the young woman. Coulson even figured that they had found a certain common ground. They found a point where they both realized that neither would ever have all of Skye. That, in one way or another, they were both fathers to Skye and both not. Both men would give anything for her. It may not have been what either man wanted, but there was nothing they could do that wouldn't hurt her. And that was the last thing either of them wanted. Still, Coulson could be happy with the way it had ended up. After all, in the end, she was with him. She could have chosen differently, lord knows she had plenty of other options. He could take the win with joy and humble pride.
Skye had every right to check up on her father, no matter how unorthodox it might have been. He could deal with some hurt feelings every now and again. It wasn't like she was doing anything wrong. But Coulson worried. When it came to Skye, he always did. Still, he wouldn't say anything after all, what outcome could he really hope for. That she let go of the man who gave her life? It didn't feel like the right thing to wish, no matter how often or loud that little voice in the back of his subconscious told him to. As long as she wasn't hurting herself or anyone else, he could let her have this.
He just closed the laptop screen and pulled a blanket over her. He knew why she had tried to keep it secret, and personally he would rather not have known. But in a way, he was happy that he did. It rang in him that she cared enough to not want to hurt his feelings, however childish it might sound. He loved the young woman dearly and he wanted nothing more than her happiness. If this made her happy or at least gave her some peace of mind, beyond how much it hurt, he was happy for her. After all, isn't that what fathers were all about?