If you don't watch How I Met Your Mother, first of all, you need to be watching it. Second, this will not make much sense to you. You have been warned.
On the subject of Barney and Robin, or The BroTP:
I did not start watching HIMYM until Heather from Go Fug Yourself wrote an amazing analysis of Robin and Ted's breakup on her personal blog, and how she related to it on an emotional level. It made me think that it was worth checking out a half-hour sitcom that could inspire someone whose writing I secretly hold as a gold standard to delve so deeply into her own psyche. At first I just watched random episodes that I channel-surfed across. Then I watched a few episodes online. Then I was watching it every Monday night. Then I Netflixed all of the past seasons that were available and watched them all in a row. Pamala and I started having more and more frequent discussions about the show and the relationships between the characters. These discussions became almost entirely about the dynamic between Barney and Robin. They were sometimes even fan fiction.
Somehow these two fictional characters became an integral part of my life. It could be that these two characters are so well written and so well acted that they seem completely real. It could be (and most likely is) due to my own relationship being at a complete standstill. Whatever the reason, I now find myself completely emotionally invested in Barney and Robin.
When they first kissed, I was thrilled. Then when we found out that they had sex and were going to pretend they didn't (not that it lasted long), I was actually disappointed. I felt like all the build up that the show had been giving us should have led to something more that just a hook-up session. But now I've learned not to underestimate these writers. The direction that they are taking this has me completely on board and convinced that Barney and Robin should be together somehow. It's been there all along. They just didn't see it. Well, ok they did a little (Zip, Zip, Zip), but not at this level. Not when there are real feelings and emotions involved.
There are certainly arguments against these two people getting into a relationship. Barney is not the type of guy who could settle down with just one woman. Robin is not the type of girl to settle down with anyone at all. But there are deeper reason why these two are perfect for each other. They would certainly not be a perfect couple, and the show would suffer if they were. It would be completely against their natures, and Lily and Marshall already have that perfect couple thing going on.
One point is that, although Barney pointed out the reasons that he and Robin would be great together when he mistakenly thought Robin's invitation to play Battleship was a euphemism for sex, those reasons don't apply anymore since both people have gone through significant changes. While this may be true, there are reasons they they should be together that are more meaningful. I think that the reasons they are really good for each other are not necessarily the reasons that Barney stated why they should sleep together. They both secretly want someone they can depend on, but they're scared of getting hurt. Robin is more cavalier about her life, so she has opened herself to the possibility of getting hurt from relationships, but not to the point of being "dependent" on someone via marriage. Barney was utterly crushed after Shannon dumped him, as we can see in that video where he looks like a hippie and is singing and crying about Shannon. Her rejection crushed him and he has been protecting himself from that pain ever since by using a persona that is not really him. His emerging feelings for Robin are evidence of cracks in that hardened shell. She is bringing out the real him; the vulnerable, human Barney.
Conversely, I think that with Robin becoming more independent and stable again with her new job (that Barney got her...), she will be more open to a relationship since it will not mean depending on another person. That seems to be when she does her best with emotional situations. When she is depressed, she ends up hooking up with the Naked Guy. And let us not forget Robin Sparkles. All you have to do is think about the video for “Sandcastles in the Sand” and her behavior with Simon later in her adult life. There is clearly a side of Robin that is just as vulnerable and fearful of rejection as Barney. They have both developed personas to help them ward off potentially hurtful situations, and that is what I think will ultimately bring them together. It seems to be almost like they recognize themselves in each other.
Unlike the rest of the group, Robin seems to really understand that there is more to Barney than what meets the eye. She seems to accept all of the different aspects of Barney without question. Lily is certainly aware of Barney's more human side, but it came as a shock to her. Marshall and Ted still see Barney as a character, even though he has done incredibly substantial things for both of them.
We certainly know how Barney feels about Robin. Throughout the show, he has been much more aware of what is going on around him and what other people want than the other characters (especially Ted). He is almost preternaturally aware of Robin, even from as far back as season one. He immediately picked up on Robin having feelings for Ted, even while Robin herself was still in denial about it. Throughout the show he has mentioned things about her that the others did not seem aware of. Like the fact that she has an occasional cigarette when she's relaxing in the tub. Whether or not he is inherently that perceptive, it is definitely something that he would have honed to a fine edge while developing his skills at picking up women. He sees what they want, what will make them happy, and he becomes it. He gives others pleasure, but he doesn't ever partake for himself beyond a superficial level. I think the thing that is freaking him out with regard to Robin is that she has the potential to make him happy, and he hasn't experienced that since he was with Shannon.
That brings us to the question of whether or not Barney could make Robin happy. Clearly the Barney that sleeps with a different random woman almost every night through various ruses and games would not be tolerated. But what about the new Barney, the bundle of raw emotions? The Barney who smashes tvs when he learns that Robin is sleeping with Ted again? How would Robin feel about that Barney? Keep in mind that Robin did date Ted for a long time, and he is about as sentimental as you can get. Also, the boost to Barney's ego that would result from Robin accepting him would bounce him right back to the level of awesome that we know and love.
The only thing that still remains in question is how Robin actually feels about Barney. My pet theory is that Robin has feelings for Barney as well, but she is not letting herself acknowledge them. I hope that as Barney's feelings for her lead him to action, however subtly, she will become more receptive to him. My fear is that she is completely aware of how Barney feels about her, but she feels nothing for him beyond friendship, so she is avoiding the whole topic. I alternate between these theories every single time Barney and Robin interact at all.