Generally, there's a lack of visible intellectual role-models so anti-intellectual messages (even the subliminal ones) win out. The media reflects but also creates our society. Our TV-dominated, sport-obsessed culture celebrates a select few skills like movie actor/actress, singer, pro footballer or wrestler. This media rarely grants time to any intellectual or technical careers in a non-derogatory way (except maybe Mythbusters & CSI). In the end we get saturated by 'Who's-dating-who in Hollywood' because we watch the stuff. The sad part of this cycle is that media folks then avoid more intellectual topics because they think the audience won't care about them. The best role models are probably teachers and parents, so teaching needs to be a well rewarded and respected, career and parents must lead by example.
Recently, we have also seen a dangerous anti-intellectual trend in conservative politicians, as science highlights many 'inconvenient truths' conflicting with their thinking.