Yes, tax inversions, in my opinion, are unpatriotic. The corporations are fleeing to other countries for getting out of paying taxes. Tax inversion shows that the corporations are not grateful to the country where their business flourished. They enjoy all the benefits of paying taxes but when the time really comes to pay the country back, they are reluctant to pay their fair share.
The usual definition given by economic times lexicon of Tax inversion, or corporate inversion, is"The relocation of a corporation's headquarters to a lower-tax nation". Now if by moving your saving jobs for Americans and helping them then no but most of the time it is because you are not pumping the vast majority of earnings like capital gains back into this country. The White House recently said they find it to be unpatriotic and want to try to change the code.
If corporations use tax loopholes to avoid paying taxes to the American government they are not contributing to the economy that fuels them. The freedom that exists within the United States of America is what allows them to exist in the first place. By avoiding paying corporate taxes they are being ungrateful and unpatriotic.
Companies switch over to other countries to earn more cash for investors. The cash that is saved by not having to pay as much in taxes is used to reinvest in the company itself. In a couple of years, the money will grow and be paid to investors as a declared dividend. Over the long run, investor will pay taxes from the dividends they have received. Eventually, this tax revenue will far outweigh the taxes the companies would have paid. Additionally, whenever the dividends are received by the investors, they will spend it, employing fellow citizens.
Big corporations are under a lot of stress to make money from investors and their big employee base. Sometimes, the big corporations need to find ways to save jobs and continue to make their investors happy or they may risk going bankrupt. Tax inversions aren't the ideal way to do this but they are far from being unpatriotic.