Privacy, reliability, security.Meaningless, unless you explain in what way.
I thought it was obvious, but...
Privacy: Some may want their mail to not be stored on a remote server where others might access it. See the e-mail bit
regarding data retention. Whether this applies solely to e-mails stored on ISP servers, or on all e-mail traffic passing through their network, someone else can enlighten me.
Reliability: A local mail server rather than a remote one will have less of a demand on it, so in theory will be less likely to fail. Weaknesses of in-house, as you put it are not something that can be addressed by residential users as there is no SLA (in many small business setups too). A repetitive problem will generally result in a customer leaving, rather than seeking compensation (which will be unlikely).
Security: Different from privacy. ISP mail servers will be higher profile targets for physical and virtual attacks, be they DDOS, spam and the rest. A local server will have a far smaller online footprint and be less susceptible to targeted attacks. Additionally, local e-mail filtering systems will be better configured to the local userbase, rather than using an ISP filtering system, which may block legit mail, or allow illegitimate mail (useless in other words).
It's all relative of course. Some folk are paranoid. Some are possibly exchanging mail with people on the fringes of the law. Some might just be geeky and enjoy the exercise, or they might have setup a system for a number of people in the house.