The message it sends is that having a gun in your house makes it more likely for you to commit suicide. But causation can just as easily be reversed, i.e. if you are suicidal you're probably more a lot more likely to acquire a gun. Would it be surprising that someone who wants to die is more likely to have something that can help him do just that?
US has a narrow definition for death by suicide that requires knowledge of intent. Compare the US definition with the UK definition.
US: "Suicide is a death caused by self-directed injurious behavior with any intent to die as a result" https://www.cdc.gov/violenceprevention/pdf/suicideTechnicalP...
UK: "this includes all deaths from intentional self-harm for persons aged 10 years and over and deaths caused by injury or poisoning where the intent was undetermined for those aged 15 years and over." https://www.ons.gov.uk/peoplepopulationandcommunity/birthsde...
> The message it sends is that having a gun in your house makes it more likely for you to commit suicide.
Yes. It's well established in suicide research that preventing access to means and methods is an important suicide prevention measure. Which suicide prevention research have you recently read?
"Men who own handguns are eight times more likely to die of gun suicides than men who don’t own handguns, and women who own handguns are 35 times more likely than women who don’t."
https://med.stanford.edu/news/all-news/2020/06/handgun-owner...
:-(
Also:
"Sixty percent of deaths from firearms in the U.S. are suicides."
So if somebody dies from a firearm in the US it's more likely to be suicide than other firearm related death.
https://health.ucdavis.edu/what-you-can-do/facts.html