The primary reason was that a "replacement program" would have been politically impossible, and would instantly have become extremely unpopular.
During the period of Democratic control, when Obamacare was in effect, the Republicans attacked the bill mostly from the left. Their critiques were that costs were too high, that deductibles were too high, that care quality was insufficient, and that health insurance was not available to enough people.
But, now that they're in power, they been hoist by their own petard--they cannot produce a set of policies that actually provides better, lower-cost, more widely-available healthcare. Obamacare was politically easy to be against, but no replacement policy that was acceptable to conservatives could actually produce better outcomes than Obamacare did, and still allow the elimination of the new taxes that were passed with the original bill.
So the Republicans were caught between a rock and a hard place. They had built a political consensus within their party to repeal Obamacare, but had not even arrived at a set of goals and principles for a replacement policy. If you look at the original ACA bill in February, these internal Republican contradictions prevented its passage. The second, somewhat modified, replacement policy that did pass the House was sold not on its policy benefits, but on the political calculus that each Republican House member had to "take one for the team" to get some bill--any bill--passed for the good of the Party.
The repeal bill originated in the House because it is the more conservative of the two legislative bodies, and because Paul Ryan, the Speaker of the House, had a bill at the ready that could be used as a base for the new bill. It also has fewer impediments to fast passage of a bill (e.g. more polarized committees, no traditions of filibuster or unanimous consent).
Senators are not as reliant on party apparatus for their seats, and tend to be more moderate than their House colleagues because they must represent a larger constituency (an entire state, rather than a more homogeneous drawn congressional district). So, the resultant bill is more likely to look more like Obamacare than what the House produced: when the two bills are reconciled between the House and Senate, support from the House will likely drop below the majority needed to pass it.