Why does upward sloping time series curve imply it is not covariance stationary and any problem for this time series analysis??

yes, that would be bad

Covariance stationary means that the mean of the time series is constant. If it’s sloping upwards, it’s not constant. It’s not so much a problem as something that can be easily remedied by differencing the time series or fitting the trend.

You need to convert it to covariance stationary and then test for AR 1 and AR 2

It’s not bad if it’s a linear or log-linear time series, y = b0 +b1(t) +E. That doesn’t require mean reversion if I remember correctly. If it’s autoregresive, it needs to have a mean reversion (and not a unit root ie b1 must be significantly different from 1)