The proximity effect is theoretically studied for thin and massive pure ferromagnet/high-temperature superconductor (F/HTS) contacts. It is shown that there is no continuous matching between the $s$-wave and $d$-wave pair amplitudes at the HTS/F boundary. In thin HTS/F nanostructures, the exchange field strongly suppresses the averaged $s$- and $d$-pairing and leads to the competition between BCS and FFLO scenarios of superconductivity. On the contrary, in massive HTS/F contact, the exchange field has no effect on the critical temperature $T_{c}^{d}$ of $d$-wave pairing. This is due to the lack of $d$-wave pairing in F layers, resulting in full internal reflection of $d$-wave pairs even from the perfectly transparent HTS/F boundary. The $s$-wave superconductivity localized at the HTS/F interface is predicted.Spontaneous symmetry change of the order parameter at the HTS/F interfaces from initially $d$-wave type to $s$-type becomes possible for massive HTS/F contact. It qualitatively agrees with experimental observations of the mixture of $s$- and $d$-wave components at the Ag/BiSrCaCuO and Fe/Ag/BiSrCaCuO interfaces.