For allowing these times to be be subject to fluctuation is inappropriate for the Torah, in addition to creating a foundation for all of the person's behavior to be erratic. Hillel's approach of flexibility and concessions might lead one to be careless in the way he relates to others, since they are supposed to be forgiving and yielding. With this, Shammai has complemented the lessons taught by Hillel, and together they present a complete picture of the way a person should behave. In interpersonal matters, one should not be strict and demanding, but flexible and compromising. However, in spiritual matters one should be strict and meticulous.
Scrupulous care is the proper approach to all matters relating to Torah study and principles.
And since Shammai had an inflexible, strict personality, his opinion was that one should always be strict. Rav Yisrael Salanter writes quite strongly against this interpretation. It was an ideological and intellectual argument between them about the proper way to serve G-d. Had Shammai agreed with Hillel ideologically, he could and would have modified his behavior in line with the correct way one is supposed to serve G-d. And if Hillel had been convinced, intellectually and ideologically, that Shammai was correct, he would have behaved exactly as Shammai did.