It wasnt so much that he was against the general defense industry per-se. He recognized the need for close cooperation between the government and industry to meet evolving defense needs.

See this passage, he above all was concerned that such a ramshackle and up and down mobilization as had been required in and leading up to 1917 and 1941 never occur again.

Until the latest of our world conflicts, the United States had no armaments industry. American makers of plowshares could, with time and as required, make swords as well. But we can no longer risk emergency improvisation of national defense. We have been compelled to create a permanent armaments industry of vast proportions.

But he also thought it needed a strong guiding hand that could keep them in check to keep bad actors at a tolerable level that meant it was still a net benefit.

Ike felt that he was just such a strong hand, but that Kennedy was not, thus raising the stakes and his calling it out. After all Ike was a General of the Army, and victor over Nazi Germany, JFK was a young senator from an old family with a less than clean record whose notable leadership experience included getting his PT Boat run over by a Japanese destroyer.

He also was involved with a cut in the size of the conventional military. His "New Look" shifted resources from conventional forces to an increase in the strategic nuclear forces such as SAC. And the threat of overwhelming responses as deterrent. However this also made proportional responses difficult to threats that were not quite worth a nuclear war. But conversely were born out of Ike's desire not to try to challenge the USSR on a tank by tank, bullet for bullet basis and deal with the attendant economic burden.