I would like a manga where the girl is smart and defends herself. For example, she isn't weak to the guy, and defends herself. She is on equal footing with him, for example he scolds her, but she also scolds him. I don't want anymore of a guy saving a girl or always protecting her. I want them to be on equal footings.
If she was dense, I want her to also be smart. Meaning: she would feel something is off, even if she can't decide if it is love, she can still catch hints.

Tonari No Kaibutsu Kun: Everything about this manga was perfect. She was also a bit dense sometimes, but other times she was very smart. Also, many times she did feel something was off because of the way certain people acted.
Manga that satisfied this in me:

Horimiya: Wow! This manga was just so realistic and I love it so much! They were both able to catch hints, and they weren't stupid when it comes to life and romance. This manga is ideal for me, and I want something like this.

Manga that was close and I wouldn't mind reading something like it:
Koi Dano Ai Dano: She was cunning and very perspective. She always argued back, and she scolded the guy many times. The guy was arrogant but then with her he became gentler. He also helped her out many times, and with him she changed for the better as well. She was dense when it comes to love but in a very realistic way: at first she lost her composure, but then she calmed down after talking to her friends, and then romance made her better, because she opened new doors.

Please don't suggest me something like Ouran: don't get me wrong, I loved Ouran, but it doesn't fit my description.

How about these:

Complete:

Ashita no Ou-sama (Theater and script writing. The two mains take each other seriously, but I'm not sure they're on equal footing until the last few parts of the manga.)

Beast Master (This should fit fairly well.)

Kare Kano (This one also fits)

W Juliet (I pretty sure this one works too)

Ongoing:

Takane to Hana (This one should fit perfectly)

Cheese in the Trap (This is college life and a manhwa, but otherwise fits the others you've read.)

Must Read Webcomic:
Unsounded

Lists:
Reading
Complete
Western Webcomics

A bunch of historic/fantasy:
Basara
Umi no Kishidan
Joou no Hana
Saver
Akagami no Shirayukihime
Gu Fang Bu Zi Shang
Okoborehime to Entaku no Kishi

And a couple others:
SA
Hana no Kishi

I've gotta suggest Koi Dano Ai Dano and the prequel Warau Kanoko-sama
And maybe Beauty Pop, Dengeki Daisy, and other works from MOTOMI Kyousuke. Hmm, maybe also Shinigamihime no Saikon, Akagami no Shirayukihime, Okoborehime to Entaku no Kishi and Akatsuki no Yona.

I also second everything mikako17 and empressasuka mentioned. Oh, look, repeats...

Ghost Hunt fits your relationship description really well. It's a very solidly written shoujo horror series with an amazing cast of characters and while its focus isn't romance, this doesn't detract from enjoyment of the series in the least. (I'd say it actually makes the two main leads' dynamic even more refreshing and interesting.) I personally prefer the anime for the art and ambiance, but the manga is great as well. It seems like we look for the same things in characters so I'd definitely suggest this one.