I'm trying to follow your logic here. So you're saying Kerensky was from a faction with limited support and found the ongoing war a convenient excuse to not hold new elections that would replace him? So the PG was trying to prolong its members' personal stay in power but dressing it up with a 'national interest' excuse of "we can't hold elections and seat constituent assembly too soon because the war is on"? Who might have been picked other than Kerensky or a member of his faction? Would they do different and why? Also, even if delay in elections is still in his self-interest, along with continuation of the war, why does this make an offensive in particular absolutely imperative?
The political strategy adopted by the Kadets and Trudoviks was dictated by war and ideology.
Aside from classical liberal reforms such as freedom of speech and assembly, they were ultimately after a new “responsible ministry” (
otvetstvennoe ministerstvo) accountable to a new Constituent Assembly or Duma, consisting of representatives chosen by universal suffrage. Since they knew that the old ruling elites would never allow the left-wing radicals to share power under such reformed system of government, the liberal strategists therefore concluded that the liberal opposition forces would be the primary beneficiaries of all political reforms, being the only acceptable alternative to left-wing revolutionary anarchy. Thus, it logically followed that in a free and fair elections, "the flower of the Russian intelligentsia" would dominate. The fact that the masses were uneducated and confused in 1917 made it all the more important from the Liberal point of view to "educate" them and postpone elections until they would see the error of their ways and vote proper liberal parties, their true benefactors, to power. The fact that Kadet was a minor nobility-dominated party really affected their worldview. Trudoviks were rather similar in their views - they pursued politics that they viewed as best for the people, while also supporting the continuation of the war to defend the new freedoms of Russian society.
The middle- and upper class liberals had passively resisted the autocracy and had longed for a constitutional monarchy or better yet, a republic, since 1905. The wartime formation of the All-Russian Zemstvo Union and the Union of Cities were both necessary wartime adaptations to the ineptness of Czarist authorities, and clear Liberal challenges to the pre-war status quo. To the most ruthless liberal leaders, the left-wing terrorists had been seen as useful allies as long as the Czar had been in power. But these liberal leaders had no illusions what would happen after they would reach their reformist goals and gain power in the country through free elections. When they would no longer neither need nor tolerate left-wing terrorism, they had no qualms about supporting the same harsh repressive policies they were now publicly condemning, as the July Days showed. To the Provisionary Government, winning the war was a key goal, since they wanted to reform the Russian society according their own vision. Ceding power to the most radical left-wing political forces was in conflict with this vision, since it would jeopardize the vision of a liberal, free Russia. One has to remember that everyone was following the only historical example that was available: the French Revolution. To the educated Russian middle class, the brave young anarchist and social-revolutionary
sans-
culottes should now stand aside, and let educated men conduct sensible policy for the good of the country and the people.
According to Kerensky an offensive was necessary because the new revolutionary zeal would inspire the Russian armies, just like it had allowed the French revolutionary armies to triumph. And a victory in war would also validate the policies of the Provisionary Government and allow them to guide the masses to reason (and to a Liberal electoral victory in the Constituent Assembly elections.)