Let's start with the dual axes. On the left, age, and on the right, year of birth. I actually like this type of dual axes. The two axes present two versions of the same scale so the dual axes exist without distortion. It just allows the reader to pick which scale they want to use.
It baffles me that the range of each bar runs from 2.5 years to 7.5 years or 7.5 years to 2.5 years, with 5 or 10 years situated in the middle of each bar.
Reading the rest of the chart is like unentangling some balled up wires. The author has created a statistical model that attributes cause of death to male life expectancy in such a way that you can take the difference in life expectancy between two time points, and do a kind of waterfall analysis in which each cause of death either adds to or subtracts from the prior life expectancy, with the sum of these additions and substractions leading to the end-of-period life expectancy.
The model is complicated enough, and the chart doesn't make it any easier.
The bars are rooted at the zero value. The horizontal axis plots addition or substraction to life expectancy, thus zero represents no change during the period. Zero does not mean the cause of death (e.g. cancer) does not contribute to life expectancy; it just means the contribution remains the same.
The changes to life expectancy are shown in units of months. I'd prefer to see units of years because life expectancy is almost always given in years. Using years turn 2.5 months into 0.2 years which is a fraction, but it allows me to see the impact on the reported life expectancy without having to do a month-to-year conversion.
The chart highlights seven causes of death with seven different colors, plus gray for others.
What really does a number on readers is the shading, which adds another layer on top of the hues. Each color comes in one of two shading, referencing two periods of time. The unshaded bar segments concern changes between 2010 and "2019" while the shaded segments concern changes between "2019" and 2020. The two periods are chosen to highlight the impact of COVID-19 (the red-orange color), which did not exist before "2019".
Let's zoom in on one of the rows of data - the 72.5 to 77.5 age group.
COVID-19 (red-orange) has a negative impact on life expectancy and that's the easy one to see. That's because COVID-19's contribution as a cause of death is exactly zero prior to "2019". Thus, the change in life expectancy is a change from zero. This is not how we can interpret any of the other colors.
Next, we look at cancer (blue). Since this bar segment sits on the right side of zero, cancer has contributed positively to change in life expectancy between 2010 and 2020. Practically, that means proportionally fewer people have died from cancer. Since the lengths of these bar segments correspond to the relative value, not absolute value, of life expectancy, longer bars do not necessarily indicate more numerous deaths.
Now the blue segment is actually divided into two parts, the shaded and not shaded. The not-shaded part is for the period "2019" to 2020 in the first year of the COVID-19 pandemic. The shaded part is for the period 2010 to "2019". It is a much wider span but it also contains 9 years of changes versus "1 year" so it's hard to tell if the single-year change is significantly different from the average single-year change of the past 9 years. (I'm using these quotes because I don't know whether they split the year 2019 in the middle since COVID-19 didn't show up till the end of that year.)
Next, we look at the yellow-brown color correponding to CVD. The key feature is that this block is split into two parts, one positive, one negative. Prior to "2019", CVD has been contributing positively to life expectancy changes while after "2019", it has contributed negatively. This observation raises some questions: why would CVD behave differently with the arrival of the pandemic? Are there data problems?
A small multiples design - splitting the period into two charts - may help here. To make those two charts comparable, I'd suggest annualizing the data so that the 9-year numbers represent the average annual values instead of the cumulative values.