Approving nods to Prof Zeki, who writes about "Reductionism...the hate word."
For some years now I've considered myself pro-reductionist, and unashamedly so. Patterns are apparent at every level in nature but there's no magic in between levels. The behavior of a system observed at any particular level of detail can be understood in terms of the aggregation of behaviors observable in a more detailed view.
No exceptions. Everywhere we look, nature rewards the reductionist by gradually unveiling her mysteries to persistent students.
Nature doesn't have levels of detail. It's we who have to break systems up into digestible chunks and look at behaviors at various zoom levels in order to gain some understanding. We lack the mental computational power to be truly holistic. When someone says they take a holistic view, all it usually means is that they want to look at an outside, low detail view to see if they can identify regularities at that level. I've no problems with that approach. It can lead to some useful ways of predicting the behavior of a system, but it only takes understanding so far.
The "holistic" word has garnered at least a few positive connotations. It's a lovely all-inclusive, I'm-a-big-picture-person type adjective to apply to your field of study, but a holistic approach needs to be acknowledged as a superficial study. It's an approach that will leave lots of unexplained results and provide a model that lacks any suggested mechanisms for more detailed study.
In my experience the holism advocated by anti-reductionists is not actually a rejection of the discipline and methodology of reductionism, but a rejection of the possibility that the system under study might be reducible -- a premature conclusion driven by ideology, not evidence.