"The bomber will always get through" was a phrase used by Stanley Baldwin in a 1932 speech "A Fear for the Future" given to the British Parliament. His speech stated that contemporary bomber aircraft had the performance necessary to conduct a strategic bombing campaign that would destroy a country's cities and there was little that could be done in response. It concluded that the conduct of future wars would require one to "kill more women and children more quickly than the enemy if you want to save yourselves."
At the time of the speech aircraft performance was rapidly improving and new techniques and construction methods were producing ever-larger aircraft. For a time, this resulted in a performance gap where multi-engine aircraft outperformed the single-engine fighter aircraft that would have to intercept them. This gap could be further widened through the use of night bombing, which made interception practically impossible.
This state of affairs was relatively short-lived. By the mid-1930s the same techniques were being applied to fighter design, once again handing them a significant performance advantage that allowed them to chase down even the fastest bomber aircraft. During the same period, the introduction of radar created an early warning system that gave interceptors sufficient time to climb to altitude before bombers arrived. The Battle of Britain suggested Baldwin was no longer entirely correct; many German bombers did get through, and did cause much destruction to British cities, but did not come close to destroying Britain's manufacturing or morale. Additionally, many bombers did not get through, being destroyed in the air. The rate of losses forced the Germans to abandon the campaign after a few months. Use of poison gas was not seriously considered by any nation, as immediate retaliation in kind would render this escalation pointless.
But later, Britain and the United States did produce enough bombers such that enough got through that a fair part of Germany's industrial production was hindered, albeit at high cost in bomber losses, and mostly only toward the end of the war, mainly because of the Allied development of long-range escort fighters capable of guarding bombers all the way to Germany.