Turn the question around. How would you feel if management had made the decision without consulting the team? At least you have a voice in the decision. It sounds to me like they're saying "This stinks, but there's no way around it ... you folks work it out."
The business decision (the BA requirement) has already been made; they're delegating the execution to the team, and that's not a bad thing.
All that being said ...
On a small team, if you're doing scrum -- or really following any kind of agile process -- the product owner and developers typically fulfill the role traditionally performed by a business analyst. Sometimes the product owner takes the lead in the analysis process, sometimes it's the developers. A BA can certainly add value -- especially if you're starting to get serious about acceptance testing -- but for small teams and especially early in the process a BA is typically perceived as overkill.
So one possible argument is that, in the process you're trying to follow, you can perform that function with the people/roles you already have. Building on @gbjbaanb's answer, you could potentially rotate the BA responsibilities between team members; it certainly can't hurt to ask if that would be acceptable. You never know, one of the devs might decide they like the BA work ... but even if not that approach of shared responsibility and cross-training is (IMHO) consistent with the spirit of agile.
Has management explained / justified the need for a BA? (You don't specify.) It may be due to some external constraint e.g. a customer is demanding it.
Or maybe the BA is supposed to be assigned to a different project. (You don't specify.) Maybe management feels you're overstaffed -- I'm not saying that's true, but it's not uncommon for a team to spend, say, 25% of its time on support activity without anyone outside of the team being aware of it.
All you can do here is attempt to quantify the impact of "taking away" a developer e.g. "that would delay the implementation of the data feed to payroll by a month, and the feed to accounts receivable by two months".
It does sound like knowledge is highly compartmentalized within your organization. IMHO that's a problem in and of itself, because of the bus factor risk. But it's going to make it difficult to do agile effectively.
My suggestion: communicate, communicate, communicate. Find out where the BA requirement comes from. Explain the impact it will have on your team's productivity. Explain the bus factor risk. Have the team suggest/discuss alternative solutions; anything the team would be willing to live with, propose that to management.