They are called candles because they think they look (and act) like candles. Guess what, it still doesn't prove their distance. Even science disagrees: ***************** Uncertainties in Cepheid determined distances Chief among the uncertainties tied to the classical and type II Cepheid distance scale are: the nature of the period-luminosity relation in various passbands, the impact of metallicity on both the zero-point and slope of those relations, and the effects of photometric contamination (blending) and a changing (typically unknown) extinction law on Cepheid distances. All these topics are actively debated in the literature.[23][20][25][32][39][40][41][42][43][44][45][46] These unresolved matters have resulted in cited values for the Hubble constant (established from Classical Cepheids) ranging between 60 km/s/Mpc and 80 km/s/Mpc.[22][23][24][25][26] Resolving this discrepancy is one of the foremost problems in astronomy since the cosmological parameters of the Universe may be constrained by supplying a precise value of the Hubble constant.[24][26] Uncertainties have diminished over the years, due in part to discoveries such as RS Puppis. Delta Cephei is also of particular importance as a calibrator of the Cepheid period-luminosity relation since its distance is among the most precisely established for a Cepheid, partly because it is a member of a star cluster[47][48] and the availability of precise Hubble Space Telescope/Hipparcos parallaxes.[49] The accuracy of the distance measurements to Cepheid variables and other bodies within 7,500 lightyears is vastly improved by combining images from Hubble taken six months apart when the Earth and Hubble are on opposite sides of the Sun.[50] - https://en.wikipedia.org/wiki/Cepheid_variable#cite_note-tammannsandage2008-23