Do you know anything about accounting? Have you ever had to do it manually? Have you ever done it electroncally? You need to be able to speak their language.
It could save this person time, but if they are a long-hours martyr, it won't matter.
They may have trust issues and want to see the details of how things add up (or don't add up). Seriously, you could sum a column in Excel and they'll question it.
Do they use an adding machine or calculator? Have they ever had to enter the same number twice? Has this caused mistakes?
Is a staff member clinging to job and fears being replaced?
You may look at it as an investment, but if they have to purchase hardware, software and pay consulting fees, there's going to be some sticker shock.
Are they aware of anyone else who switched to an electronic system? They may have heard horror stories.
I could go on and on, but other than their lack of accounting software, you didn't mention any other problems. I've never used any tax software because I always hire someone. Maybe I will one day if I can ever file a short form.