She walked close to Gatsby, touching his coat with her hand. . .
‘Did you see that?’ demanded Tom.
‘See what?’ He looked at me keenly, realizing that Jordan and I must have known all along.
‘You think I’m pretty dumb, don’t you?’ he suggested. ‘Perhaps I am, but I have a—almost a second sight, sometimes, that tells me what to do. Maybe you don’t believe that, but science—'
Tom is a fool. Every time I read this book, I get upset with Tom, because he thinks he is so smart and so entitled. Part of his feelings of entitlement have to do with money. Another part has to do with privilege. Tom feels that he is entitled to act any way he wants. That includes cheating on his wife.
First, the quote is ironic, because it shows that Tom is upset that Daisy is cheating on him even though he is doing the exact same thing.
Second, the quote is ironic because Tom is attempting to explain to Nick and Jordan just how smart he is. How smart is he? Well, according to Tom, he has a second sight or sixth sense. Basically, he believes that he has the intuitive power to accurately read all situations and perhaps even see into the future. It's ironic and ludicrous for Tom to say such foolery, because he is the last person to realize that anything is going on between Jay and Daisy. What is painfully obvious to everybody else is only just dawning on the guy who claims he has a "second sight."
The moment that Tom Buchanan says that he has "almost a second sight" is right after he starts to put it together that there is something between Jay Gatsby and his wife Daisy Buchanan. A second sight implies ability to see future events. This has been going on for some time now. Nick had earlier mentioned in the scene how Daisy's voice was "indiscreet", the descriptions of what is happening make it all seem so obvious that there is something between them. Tom has just now figured this out. It reflects upon Tom's nature of thinking he is so clever. He believes that he is clever with his womanizing as well, but he makes it so obvious. He also follows up with beginning to argue science but stops. The concept of "second sight" and science do not fit.