We see belief in bad omen as blind and not modern. Let us see what Ramayana says. when Rama was returning after killing Marreecha (in the form of Golden deer) he was perturbed as Marreecha had called “Ha! Lakshmana! Ha seetha! help me”. He was worried that something untoward would happen. It is here that he sees bad omen and Valmikiki describes the bird crossing Rama from left to right as bad omen. The sloka is not clear (in many books) hence I have given the word by word meaning. the words in blue colour in bracketare redundent.
सव्यम् कृत्वा महात्मानम् घोराम् च ससृजुः स्वरान् |
तानि दृष्ट्वा निमित्तानि महाघोराणि राघवः |
न्यवर्तत अथ त्वरितो जवेन आश्रमम् आत्मनः || ३-५७-१३
13. [mR^iga pakSiNaH = animals, birds]; mahaatmaanam = of noble-souled one Rama; savyam kR^itvaa = on to left, making – moving on to left; [tam aaseduH = him, they on nearing]; ghoraam svaraan sasR^ijuH ca = frightening, shrieks, they let off, also; raaghavaH = Raghava; mahaa ghoraaNi = highly, forbidding ones; taani nimittaani dR^iSTvaa = those, foretokens, on observing; atha = then; tvaritaH = hastily; javena = hurriedly; aatmanaH aashramam nyavartata = to his own, to hermitage, returned.
Those doleful animals and birds moving in circumambulations from the left side to right of that noble-souled Rama they let off frightening shrieks, and then observing those highly forbidding foretokens Rama returned to his own hermitage hastily and hurriedly. [3-57-13]
Doe that mean we need to be more careful when cat crosses our path and not neglect it?