Why GDP series always has an unit root problem? In one of the lecture slides of class that I am currently taking our professor mentioned that when it comes to the GDP is it safe to always assume it has unit root and testing for it is just superfluous. However, why is this the case? Is that just an empirical regularity or is there some reason why GDP will always have unit root?

I suppose this could be due to the economic growth, but we did also learn about trend stationary series. I also understand that the reason why any series has unit root is that the shocks to the series never die out, but why wouldn't that hold for GDP? In our macroeconomics class we were always taught that business cycle shocks are transitory and ultimately GDP grows around its balanced growth path.
Whether GDP has a unit root depends on whom you ask, and what they believe about the nature of business cycle. 

The seminal paper that first applied a unit root test (the ADF test) to macroeconomic time series and extracted economic implication is Nelson-Plosser (1982).
They were unable to reject the unit root null hypothesis for GDP and other standard macro series. They offered the following conclusion:

"...macroeconomic models that focus on monetary disturbances as a source of purely transitory fluctuations may
never be successful in explaining a large fraction of output variation and that stochastic
variation due to real factors is an essential element of any model of macroeconomic fluctuations."

These are fighting words in the debate of Real vs. New Keynesian Business Cycles. They interpret their finding as evidence against the latter. Or at least that variation in output is more attributable to permanent real shocks rather than transient shocks to aggregate demand ("monetary disturbances").

Later, however, in a subsequent milestone result Perron (1989) found that a trend-stationary series with a break in its deterministic trend may be mistaken as unit root. In particular, he overturned Nelson-Plosser's non-rejection result for GDP (and other series), after taking into account the 1929 crash and 1973 oil price shock. 

Another possible example of such trend-stationary series with structural break is the CBO GDP data series covering the Great Recession shown in answer by @1muflon1.

Today, the suggestion that, say, US GDP of the last 20 years has a unit root would probably not be too controversial.
In general, the answer you get depends on the data, the unit root test being applied (there are many), and whether the economist has a strong RBC or New Keynesian bias. 

(For example, Nelson and Plosser were already RBC advocates before publishing their finding.)