1.  It is a mental health problem.  This is by definition certainly true.  But recent shooting instances could not always be predicted by the observed mental health of the shooter (Las Vegas shooting was the worst in our history and the shooter would never have been identified as deranged with current standards based on his behavior prior to the shooting).  But more importantly  there is little help or sympathy at the governmental level for the mental health services where there is often no question of need.  The debate over how and who to identify with mental health issues will be endless and is unlikely to produce anything more than a few band aid type changes. There just is too little science to rely on and even less money available to implement existing science and politicians show no signs of increasing this spending.  This argument also requires background checks and the failures of current background checks are often sited when these mass murders occur.  More regulations, if implemented, require more administration.
2.  Existing gun legislation keeps law abiding citizens from protecting themselves and others.  This is partly behind the current congressional effort to permit anyone with a legal right to carry a gun in their state of origin to carry in any state.   There are 12 states with essentially no limits to carrying weapons.  Such legislation would seriously threaten those states that do regulate guns*.  This is a curious argument that essentially plays into the hands of the gun lobby if for no other reason than it would result in more weapons sales and more profits.
3. More armed security guards,  more armed teachers, more armed business owners, more armed people everywhere.  This argument is also part of the agenda to sell more guns and make more money.  However the principle failure  in this line of reasoning relates to the fact that guns, particularly lethal examples such as AK-47s and other automatic weapons and their accessories designed to multiply their effectiveness  and lethalness  are offensive weapons.  They give an advantage to the first user that often can’t be overcome by those with weapons for defensive purposes. And very few defensive weapons match the fire power of a well-armed and determined owner of mass casualty weapons..
4.  Gun regulation is not permitted by the 2nd amendment.  The second amendment calls for a “well regulated militia” which the gun lobby and their political allies usually prefer to interpret as “little or no regulation”.   The second amendment is not “final” and there may be correctable flaws in the language.  That is why the founders provided a mechanism to amend the constitution and/or its amendments.  In the case of prohibition, a constitutional amendment was actually abolished.
5.  Gun regulation means that only criminals would have guns.  This statement is a particularity heinous argument as on the surface it appears to be true. Ample evidence exists that many weapons in the hand of those likely to use them for nefarious purposes were obtained through legitimate channels. At the very least fewer criminals would have weapons even if some still managed to find their way into the wrong hands.
6. There are too many guns in the hands of citizens.  No laws can possibly have much effect on guns that are already out there.  This is essentially an argument that says change can not be done and "reducing gun violence" is impossible.  Yet much evidence indicates that perpetrators of gun violence are often using weapons only recently acquired, especially when assault weapons are used.  So tightening gun purchase requirements could be expected to reduce access to those who should not be acquiring weapons.  But more logically, any reduction in gun violence would be welcome.  Even if relatively few lives are saved or changed, would this not be worthwhile?  But evidence from countries like Australia which cut off easy weapon acquisition suggests there would be big reductions in gun based violence.   And in the U.S. during the 10 year assault weapons ban dramatic reductions in gun violence deaths were recorded.*

When confronted with the horrific crimes associated with gun violence, politicians supported by the gun lobby use a form of argument  known as a “red herring” argument.  A “red herring” argument is an argument that changes the subject and  is mainly used to divert attention from a more direct and useful solution that is unpopular with a particular constituency.