Based on the previous chapters, the MC already knows that the step-mother and his step-brother have both been trying to get him killed several times. Poison through food, attempts to kill him via assassination, trying to ruining his business (and his father's finances), etc. Even the trigger point of the announcement of being heir to the family, they outright planned to kill him there as a means to solidify control over the family.
The MC believing the bullshit about the step-mother and brother "not going to kill you because we're family" at this point is dumb. It would've been better written if the MC exposed all of the attempts they've been hiding from the grandparents and his own parents, some of which were witnessed by his childhood friends (he was even hung on a tree to be beaten to death before in front of them). Then it would've been more understandable for his grandparents and parents why he had to eliminate them there.
I have a feeling that Goddess is also a reincarnated person or someone entirely different from what the people of that world think she is. Last time she had a line speaking, it sounded like she was having "ecchi time" with the Demon Lord rather than fighting him.
They've been trying to assassinate him behind his parents' and grandparents' backs for years, thinking he was easy prey. Never did they think he would fight back against them.