I recently wrote this up for our house fellowship congregation.
First, Saturday's setting sun marks the beginning of the Lord's Day -- or Lordsday as I like to spell it -- according to YHWH's creation ("So the evening and the morning were the first day."). So, we are gathering on the Lordsday. It's not according to modern man's reckoning, but according to the Scripture, we are. For me personally I think both of these points are important. One of the places this is modeled for us specifically is in Acts 20.7-12.
Second, we gather to "break bread" together. To gather around an agape meal together -- which is a meal with the celebration of Communion within it -- is the main focus. It is not to "get to know one-another", or to study the Scriptures, or get warm fuzzies and good "feelings". Now, while an agape meal is modeled and taught throughout the New Covenant Scriptures as the primary reason we gather together as believers (1 Corinthians 11:18-33) it is, at the same time, not the only reason. Others are integral to the gathering time as well: studying the Scriptures, encouraging one-another, singing and praying together (1 Corinthians 14.26; Acts 2.42); but the coordinating of gathering around a meal is what might be called the "congregating factor". That being the case, then an evening meal at the end of our work day allows us to begin to savor the aroma of leisure that our time together should be marked-out by due to what we confess: That we have assembled together to celebrate and rest in our King's life, death, and resurrection. An evening meal accentuates and stamps that truth on our hearts more than any other meal because it is at the end of the day when we typically have no other plans to preoccupy or distract us as they normally would if we met in the morning or lunch time (and I've done both, and they do). And an added bonus is since the next day is the full Lordsday, which most Christians have off from work responsibilities, it allows us to stay longer and not have our time cut short but rather be peacefully maximized and redeemed.
Now, as a counter-example, we could gather for a lunch meal in the middle of the Lordsday and then proceed as we normally do, but often folks have daytime commitments even on the Lordsday and they're distracted and time-constrained; or perhaps someone may have a sense that the day-light is being "wasted" and will endeavor to leave as soon as possible. I've encountered both types. This, though, is just another reason why an evening meal works so well because not only is it theologically sound, but it is eminently practical as well.
Third, the Lordsday needs to be a day of sabbath, a true heart and body REST. Six days we labor and then we rest. We rest on the first day because it is the day He completed all the work that was to be done on our behalf and rose as the King of the New Covenant. As I tell my family: "The Lordsday is for us, to turn away from us."
To gather in the middle of the Lordsday not only makes real body and mind rest nearly impossible, but ultimately whomever is hosting the gathering will not likely receive any whatsoever! In all our pasts, when we all went to BoxChurch Inc. we never felt that weight, but gathering as a house congregation is an added weight and responsibility to all of us, host home or not. At BoxChurch Inc. we could just show up (after stressing-out to get there on time!), sit, and go home. A few "someones" bore the work. Not in a house fellowship.
So, let's say for arguments sake, that we did gather in the middle of the Lordsday and that we'd alternate the host home every time we gathered so that we could spread out the responsibility and work.... well, that still leaves one home/family exhausted at the end of their one Day of REST for the week, and over time this collectively takes its toll on the whole congregation. Little by little families aren't having a needed rest (even if it's one Lordsday out of four or perhaps six) and it slowly builds and soon the work and exhaustion manifests itself in our lives through a myriad of ways. And the Lordsday evening (Sunday evening) isn't any better because almost everyone has Monday responsibilities that demand that you cut your time short and head home early to get a full nights sleep; this just has everyone watching the clock which stifles discussion and the free-flow of koinonia.
To sum up: we gather at the beginning of the Lordsday to celebrate an evening agape meal of leisure that impresses upon us the reality of Messiah's work on our behalf and the rest He has given. It is an evening of no distractions nor commitments which promotes peaceful fellowship and worship; this leads into opening for us, on the next morning, the blessing of a FULL Lordsday for mind and body rest.