One IOD that I have been getting from many women, and sometimes more than once from the same woman is this:

They are afraid to say no.

Which is actually a bad thing, because it instantly turns communication into shit.

Examples: I ask them on a date. They say yes. They either then cancel or no-show.

I offer up a date...They completely ignore the offer, and change the subject.

Or I offer up a date and they give a "maybe" and then wait until after the day comes and goes and try to continue on conversating as if that exchange never happened.

Worst case scenario: I messaged on the day and said "hey you told me today would be good for dinner. I'm thinking this restaurant..." and she replied, "Who is this?"

This last woman said "I am not available weekends. How is Saturday? (on Saturday) I can't make it. (10PM that same Saturday while I'm with another woman) Nevermind, I can make it."

I guess some of you guys will say that's a hint that I am not building enough rapport...but why would I want to have any sort of relationship with someone who is a flake, can't make plans, or just seems completely disinterested?

I guess what I am looking for is how to handle the feels I get from going through all of this...

This is a huge question because it is precisely what makes a lot of guys get out of the 'game'.

It can be shitty when you have a GREAT first interaction with a girl, etc etc and she flakes or doesn't even reply to your text.

You can get better by forming a closer bond in your initial approach, not necessarily through time invested but through your actions.

You can also alleviate this by simply meeting more women and going up the learning curve in terms of how to be more warm and obtain the responses you are after.

Bottom line, it's a big world, there are a lot of things vying for her attention and you need to be memorable and form a warm bond with her so she wants more of that. Sometimes even that isn't enough.

2 choices:
1) Meet more women and continue to get better at this.
2) Quit like most guys do who end up settling before their time.

Yes, brother. I feel you. I live in Asia, where it is culturally rude to say no to someone, so I also experience this from time to time. I would advise that when you are getting to the date setup, you make a specific day to confirm and adjust if needed. If it is Saturday and you ask for a date next Saturday at a specific time and place, you need to be checking in during the week, and have a firm restatement of the time and place before the end of Wednesday. If you are building rapport and staying engaged with her, she will be much less likely to blow you off. You could have met some flakes, but for most people, if you are being a worthwhile chat partner, they should be interested to see you in person for the date.
Good luck.