As you would expect from a lawyer trying to make a case, Taylor isn't telling the full story, especially those inconvenient bits that refute his central premise. First, he's combining Arctic and Antarctic sea ice. This is important because the two polar regions have very different dynamics. The Arctic is an ocean surrounded by continents, the Antarctic is a continent surrounded by ocean. Sea ice is all the ice the Arctic has. Up until the 1970s, most of that sea ice was multi-year ice. The Antarctic, in contrast, has around 30 million cubic kilometers of land ice to go with a mostly temporary coating of sea ice.
If Taylor were being completely honest, he would at least attempt to align the seasons between the poles before adding them together.
Of course, admitting that overall sea ice has declined, with a trend that, despite an increase since 2012, is still below its starting point won't fit Taylor's narrative. And he most definitely won't show what is happening with multiyear sea ice (the ice that survives each yearly melt cycle).
The other reason merely adding Arctic and Antarctic sea ice is wrong? The two regions have opposite trends.
Bintanja et al. 2013, McMillan et al. 2014). That meltwater is also leading to thermal stratification of the ocean around Antarctica, which insulates any sea ice from warm currents below the ice (Zhang 2007). A third piece of the puzzle appears to be stronger circumpolar winds which have opened up more gaps in the floating sea ice (i.e. Turner et al. 2009). But you won't hear any of that from Taylor. All he cares about are those facts he can spin to make his argument.
Beyond the tired arguments made by omitting most of the facts, there is little else to Taylor's piece—and nothing that is truly new. It's the real "hide the decline" trick with a different author's byline under the title. (Ambler last year, Taylor this year—second verse, same as the first). As with Ambler, it's a nice try—but he won't fool anyone who has a modicum of knowledge about the polar regions and statistics.