AITAH for trying to have my coworker work less?

I work in a small field consisting mostly of freelancers, so I'm going to leave out some details, but I'll try to explain as much as I can.

I'm new to this line of work; only started last year. I met someone who's been doing this for 10 years, and they were very nice to me during our previous project. Let's call them A. During this project, we spent some lunch breaks together and even met up and had coffee outside of work. I respected A's professionalism, and thought we could be work friends, as they were amicable enough toward me then.

This year, we met on another project. Originally, three of us were supposed to be here, but there were some complications and there are only two now. On paper, A is doing Task 1, and I'm in charge of Task 2 and 3. We thought this would be fine, but it turns out that Task 2 and 3 take up most of the day and Task 1 is more laid back.

Now, this is the part where I felt I might have screwed up: because A has told me in the past that Task 2 was the more difficult one, I thought they would rather not have to do that and only work on Task 1 and 3. I probably shouldn't have assumed this.

We usually broke the day up into four blocks: half of the mornings, half of the afternoons. I asked A if they wanted the earlier block or the later one a few times, to which they always replied I was always the one that went first, so I stopped asking them for a while.

A few days ago, I asked once more if they wanted to take an earlier block in the morning, since Task 3 was listed for that block.​ This seems to have been the last string, as they've been giving me the cold shoulder since then.

2 days ago, we had two things happening simultaneously, and because I didn't want A to have to work the entire afternoon, I said I'd take the earlier block of the afternoon and head over to do the additional task. This was when A asked if this was because I wanted to do the work all day. I explained that I felt like I was pushing my job onto her. A said they didn't understand and left.

The exact conversation went like this:

Me: I'll take the earlier block this afternoon and leave for Additional Task.

A: Oh, because you want to do this all day?

Me: No.

A: Is this (working out who's working when) that important to you? We're just splitting the day in half.

Me: (I don't exactly remember what we said between this.) But on paper it says I'm supposed to be doing Task 2 and 3, so it feels like I'm pushing my work onto you.

A: Does your contract say that you'll be doing Task 2 and 3?

Me: No.

A: Then I don't ​understand.

I was taken aback by this, but didn't take the conversation any further. A didn't seem to want to talk anymore, and my mood had been soured from the exchange as well.

Yesterday we barely talked, and we simply did our jobs.

Today, though, A started encroaching upon my work, cutting me off mid-sentence and taking over conversations. It definitely feels like they're doing this on purpose, and that their actions have some malice to them.

I know I should be talking directly to A and let them know I wasn't belittling their work or trying to take over the project. Or maybe I should just keep playing dumb and act like nothing happened. Either way I need cool my head over the weekend because I definitely was offended by A's actions today.

I do want to smooth things over eventually, though, because I know we'll need to work on other projects together in the future.

But did I bring this upon myself? AITAH for trying to make work "easier" for A?