That isn't the case. This idea is expecting cycle to repeat itself that has more variables that we had time to track. The next ice age will be far longer. Around 10,000 years from now. I will add my personal claim that it will be even longer than that, because the eccentricity will reach a very low point in 26,000 years, and I will contend the effects of the eccentricity is underestimated.
The abstract of this paper even puts earlier thoughts out as far as 1,500 years. Not now, but this paper say why it shouldn't be for another 10,000 years:
Determining the natural length of the current interglacial.
Now the abstract does say "Assuming that ice growth mainly responds to insolation and CO2 forcing, this analogy suggests that the end of the current interglacial would occur within the next 1500 years, if atmospheric CO2 concentrations did not exceed 240±5 ppmv." However, the article itself is challenging this idea. Not agreeing with it. However, the paper is not available to the general public. I subscribe to Nature Geoscience, so I have full access. The first paragraph of the paper says:
The notion that the Holocene (or Marine Isotope Stage 1, MIS1), already 11.6 thousand years (kyr) old, may be drawing to a close has been based on the observation that the duration of recent interglacials was approximately half a precession cycle (∼11 kyr; ref. 8). However, uncertainty over an imminent hypothetical glaciation arises from the current subdued amplitude of insolation variations as a result of low orbital eccentricity (Fig. 1). It has thus been proposed that at times of weak eccentricity–precession forcing, obliquity is the dominant astronomical parameter driving ice-volume changes, leading to extended interglacial duration of approximately half an obliquity cycle (∼21 kyr; ref. 9).
In this view, the next glacial inception would occur near the obliquity minimum ∼10 kyr from now.